Hampton math - Math 2



Common Core 2: Unit 5 – TrigonometryPart 1: Radical Operations and Rationalizing the DenominatorWarm-Up:Solve for x. (Simplest radical form)1. 2. 3. 4. 5. 6. Part 1: NotesBasic Radical Operations- Simplify each addition or subtraction expression. 1. 2. 3. 4. 5. 6. 7. 8. 9. Simplify each multiplication or division expression. 10.11.12.13.14.15.16.17.18.19.20. 21.22.23.Rationalizing the Denominator: Notes and PracticeThe process of eliminating a radical from an expression’s denominator is called Rationalizing the Denominator. Rule: In order to eliminate a radical from the denominator of an expression, you must ___________________ the expression by an appropriate form of the number 1. Remember that you can write the number 1 as a fraction such as . Steps to Rationalize: Multiply the numerator and denominator by the radical in the denominator. Simplify until no radical sign is in the denominator. Simplify the numerator. Reduce outside fractions. In each of the example below, rationalize the denominator. Example #1: Example #2:Example #3:Example #4:Example #5:Example #6:Example #7:Example #8:Part 1 Practice:Bonus:Part 2: The Pythagorean Theorem, Pythagorean Triples and the Converse of the Pythagorean TheoremPythagorean Theorem: In every right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse.Solve for the missing side by using pythagorean theorem. Leave answers is simplifed radical form. 1. 2. 3. 4. 5.6.7. 8.Pythagorean Triples: A set of three positive integers a, b, and c that satisfy the equation c2 = a2 + b2. The most common Pythagorean Triples are 3, 4, 5; 5, 12, 13; 7, 24, 25; and 8, 15, 17.You can create new triples using a common scale factor of a given triple. For example: 3, 4, 5 : If you multiply each side by 5, the triangle becomes 15, 20, 25. Does that satisfy the Pythagorean Theorem?Find the missing side in each ?:4572000135890d00d1447800135890a00a35814001358903500351219200215900022098002159000335280021590004343400215900054864002159000525780073025e00e3505200530225c00c198120073025b00b5486400415925004343400415925003352800415925001219200415925002209800415925005638800530225450045579120073025750075403860073025004572000530225100130480007302528002822860005302252700272514600730254500451295400530225150015838200730252000201. {3,4,5}5581650854710005762625330835e00e5334000435610600656102257880350056102251022350045148508547102500254619625330835d00d4191000435610600060446722578803500446722510223500352425085471015001536290253308353900393200400435610c00c34766257880350034766251022350022860009023353000302438400330835b00b20574004356107200722333625788035002333625102235007905751022352426a002426a2. {5, 12, 13}3810000125095210021Mixed Pythagorean Triples: Find the unknown length. 21336001060452426b002426b4800600431801630d001630d381000015748000381000015748000137160043180150015838200157480900910668004318000426720089535051h0051h61722001238250006019800438150005257800112395024002440386001238250150015358140089535020002033528001238250g00g379095014097000034575756762750021336001466850f00f251460010096501.2001.219812008953501.3001.3233362513525500021050256667500039624002095507500751295400438150a00a106680032385000358140083185c00cleft103248Which triple did you use? Write letter inside each triangle. 3, 4, 5, 5, 12, 137, 24, 258, 15, 1700Which triple did you use? Write letter inside each triangle. 3, 4, 5, 5, 12, 137, 24, 258, 15, 17 Converse of the Pythagorean Theorem: ?If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.State if each triangle is a right triangle.1. 2. 3. 4. 5. 6. Euclid’s Formula for generating triples (Honors):If m and n are arbitrary pairs of positive integers and m > n, thena = m2 – n2 b = 2mnc = m2 + n2If m and n are coprime, and exactly one of them is even, then the triple formed is primitive. (a, b, and c are coprime). Examples: Find the triplesn = 1 and m = 2 2. n = 2 and m = 3 3. n = 2 and m = 4Find the values of m and n given the triples 4. 7, 24, 25 5. 11, 60, 61 6. 40, 42, 58Part 2 Classwork/Homework:2667000114935120012Find x. Put answers in simplified radical form if necessary. 5257800166370x00x48006001663706006236220016637000315277510350550052590800103505x00x485775151130300383820074930x00x68580033210500491172510096500685800103505001. 2. 3. 50292001358901000107905755461040045181600133350120012533400190509009510540013335000228600052768500228600018478500304800704850030480070485004. 5. 6. 495300012192080085486400121920x00x205740012192010001025908007620200020609600121920110011762007620x00x2514600149225x00x5410200260352400242743200260356006457200260354004106680014033500632460030670500495300030670500541020064960500556260064960500551497578105005410200781050049530005353050049530007810500495300078105002667000781050053403574295007. 8. 9. 556260015240x00x464820015240700725336501524000320040015240x00x685800129540x00x809625320631200122286008509015x0015x5305425199390005715000656590x00x5029200656590x00x5029200380365450045502920019939045004531242008851905005259080031369050053124200313690x00x5105400469900049530004279900028289257994650035147257556500282892575565002828925755650028194008509000457200850900014478007708900010. 20. 21. 11.838200107315x00x13779597790x00x12. 21. {7,24,25}22. {8,15,17}lefttop23. Shannon and Sam left the riding stable at 10 a.m. Shannon trotted South at 10 kmph while Sam galloped East at 16 kmph. How far apart were they at 11:30 a.m.?24. Find the perimeter of an isosceles ? whose base is 16 mm and whose height is 15 mm.25. Find the length of the upper base of the isosceles trapezoid with legs of length 15, height of 12 and lower base of length 35.26. Find QD.27. Find x and y.28. A submarine travels an evasive course trying to outrun a destroyer. It travels 1 km north, then 1 km west, then 1 km north, then 1 km west, etc… until it travels a total of 41 km. How many kilometers is the sub from the point at which it started?29. Find the altitude of an isosceles trapezoid with base lengths of 2 and 20 and side lengths of 41. 30. The side lengths of a right triangle are x, x + 3, and . Find the value of x. 31. Find x. 32. Find the side lengths of a right triangle that has side lengths of x, 2x – 1, and 2x + 1. Part 3 – Special Right Triangles Notes45-45-90 Special Right TrianglesAnswer the following questions using the triangle below.9144029210001. 2. Classify the triangle by its angles and sides.3. Use the Pythagorean Theorem to write an equation in terms of x and h. Then solve for h.4. Now label AB = 5 and AC = 5 and find BC.5. Does your answer coincide with your answer to #3?SummaryIn a right isosceles ?, each acute angle would have a measure of ________. 34778958191513xy2.0013xy2.29972090170yx1.00yx1.33718503365512 cmyx4.0012 cmyx4.370840895359 cmyx3.009 cmyx3.30-60-90 Special Right TrianglesAnswer the following questions using the triangle below.-190563500001. ?ABC is an equilateral triangle. What is the measure of: 2. is an altitude of ?ABC. What does do to segment AB?3. Based on your answer to problem #2, find the following lengths in terms of x and write them on the diagram.AB= AD= BD=4. is an altitude of the equilateral ? QUOTE ? ABC. What does do to ?5. Find the following angle measures: 6. Highlight ?DBC. It is a 30-60-90 triangle. Use the Pythagorean Theorem to write an equation, substituting the side lengths of , , and . Then solve the equation for h. SummaryIn a right ?, if one acute angle has measure 60, then the other angle would have a measure of ________.3533775234950760yx6.00760yx6. 19333227305308xy5.00308xy5. 64770152400y30x7.00y30x7. 4530090698530?6xy9. 0030?6xy9. 2419350-317530?10xy8. 0030?10xy8. Special Right Triangle WorksheetUse special right ?’s to solve:1. Find the length of a diagonal of a square with sides 10 inches.2. Find the perimeter of a square whose diagonal is 4 cm.3. One side of an equilateral ? has length 6 cm. Find the length of the altitude.4. Find the perimeter of an equilateral ? if the altitude has length 9 cm.5. Find the length of a side of an equiangular ? whose altitude is 12.52578005905545hfg0045hfgUse the given length to find each of the remaining two lengths.6. g = ________________7. h = ______________8. f = 9 _________________9. f = _______________10. g = 12 _________________11. h = _______________6324600164465t00t12. t = 4 __________________13. u = ______________51816001333500563880026670u00u14. u = 10 _________________15. s = 6 _______________617220053340s00s565785018669030003016. t = ________________17. s = ______________Use the diagram to find the remaining lengths.4699635101600c6045deab00c6045deab18. a = 2, b = _________, c = ________, d= _________, e = _________19. a = ________, b = _________, c = ________, d= _________, e = 420. a = ________, b = _________, c = 10 , d= _________, e = _________Part 3 – HomeworkSolve for the missing sides in each of the given triangles using the relationships for special right triangles. Leave all answers as simplified radicals.174625198755xy154500xy15451. x = ____________y = ____________37211011303012245yx0012245yx2. x = ____________y = ____________59245581280x42y00x42y3. x= ____________y = ____________6604019050026y60x0026y60x4. x = ____________y = ____________28067010668030xy0030xy5. x = ____________y = ____________1644656604060xy280060xy286. x = ____________y = ____________488315104775xy184500xy18457. x = ____________ y = ____________4368807175560xy0060xy8. x = ___________ y = ____________4787908128012645yx0012645yx9. x = ____________ y = ____________Part 4 – Notes - Special Right Triangles: Word ProblemsLeave each answer in Simplest Radical Form.1. Ryan quit bowling and took up sailing. His sail for his sailboat is a 45-?‐45-?‐90 Right Triangle. The base of the sail is 6 ft. long. What would the height of the sail be? What is the length of the hypotenuse?2. Joe saw a “Yield” sign and “borrowed it.” He wanted to hang it up in his room because it looked cool and it was in the shape of an Equilateral Triangle. The length of one side is 34 inches. What is the height of the sign?3. Jeremy is going to show off his skateboarding ability to his Geometry class. He has a skate board ramp that must be set up to rise from the ground at 30 ?. If the height from the ground to the platform is 8 feet, how far is the ramp to the platform? How long is the ramp up to the top of the platform?60007567945004. Tristan has a square back yard with an area of 225ft sq. He started to plant grass seed but only did half his yard. What is the perimeter of the Grass section of the backyard?52387545085005. Lorena and Karla are creating an art project in the shape of a right triangle. They have a 92 cm-?‐long piece of wood, which is to be used for the hypotenuse. The two legs of the triangular support are of equal length. Approximately how many more centimeters of wood do they need to complete the support?6. Mr. Rasczyk has a tree farm. Half the farm is trees that he uses to make pencils, the other half are maple trees that he uses to make maple syrup. The farm is a Square divided into 2 sections along a 400 foot diagonal. What is the area of the Maple Tree Farm section?Part 4 - Homework – Special Right TrianglesSolve for the missing sides in each of the given triangles using the relationships for special right triangles. Leave all answers in terms of radicals.2286008953545xy180045xy181. x = ____________y = ____________71120189865x309y00x309y2. x = ____________ y = ____________3073406985045xy0045xy3. x = ____________ y = ____________4762550165x30126y00x30126y4. x = ____________ y = ____________1162057112045xy200045xy205. x = ____________ y = ____________755652286045xy0045xy6. x = ____________ y = ____________In a 30°- 60°- 90°triangle, the shorter leg is 6ft long. Find the length of the other two sides.Longer Leg = __________Hypotenuse = __________The hypotenuse of an isosceles right triangle is 10 inches. Find the length of the legs.Length of the Legs = __________An altitude of an equilateral triangle is 103 units. What is the perimeter of the equilateral triangle?Perimeter = __________Find the length of the diagonal of a square that has sides of length 30cm.Diagonal = _________The perimeter of a square is 32 feet. Find the length of one of the diagonals.Length of the diagonal = __________The diagonal of a rectangle splits the rectangle into two triangles. If the diagonal is 14 inches, find the perimeter of the rectangle.Perimeter = __________Jeremy has a skate board ramp that must be set-up to rise from the ground to the top of a wall at a 30° angle. If the bottom of the ramp is 9 feet from the wall, how high is it from the ground to the top of the wall? How long is the ramp up to the top of the wall?01905Height of Wall = __________Length of the ramp = __________Part 5 – Right Triangle TrigonometryWarm Up4391025269240x10yTRIANGLE B30°x10yTRIANGLE B30°1. For each of the triangles below, use special right triangles to find the lengths of the missing sides and record your measurements of the lines provided.060325xr2TRIANGLE A30°xr2TRIANGLE A30°5010150147320TRIANGLE Bx = __________y = __________r = ___________020000TRIANGLE Bx = __________y = __________r = ___________center146685TRIANGLE Ax = __________y = __________r = ___________020000TRIANGLE Ax = __________y = __________r = ___________180975157480ryTRIANGLE C0ryTRIANGLE C4933950104069TRIANGLE Cx = __________y = __________r = ___________020000TRIANGLE Cx = __________y = __________r = ___________357187518288030°0030°2. For each triangle, find the indicated values. Round your answers to four decimal points.4981575102235TRIANGLE C = __________ = __________ = ___________020000TRIANGLE C = __________ = __________ = ___________2800350102235TRIANGLE B = __________ = __________ = ___________020000TRIANGLE B = __________ = __________ = ___________581025102235TRIANGLE A = __________ = __________ = ___________020000TRIANGLE A = __________ = __________ = ___________3. What do you notice about the answers for question 2 from Triangle A, Triangle B, and Triangle C?Part 5 NotesTrigonometric RatioAbbreviationDefinitionSine of PSin PCosine of PCos PTangent of PTan PLabel each of the sides as opposite leg, adjacent leg, and hypotenuse.Set up the appropriate ratio of sides for each trig function. Use the Pythagorean Theorem to find the length of missing sides. 7. sin A = ________cos A = _______tan A = _______8.sin C = ________cos C = _______tan C = _______9. sin A = ________cos A = _______tan A = _______sin B = ________cos B = _______tan B = _______10. sin F = ________cos F = _______tan F = _______sin G = ________cos G = _______tan G = _______Part 5 Homework1.Label the following names of the sides to the correct positions for each triangle based on the lower-case letter θ (Greek letter theta). θ is used as a symbol for an unknown angle. O = OppositeH = HypotenuseA = Adjacenta. b. c. d. 2. Set up the appropriate trig ratio for each of the following right triangles:a. b.c.d. 3. Find the following trig values using the calculator. (Make sure you calculator is in degree mode and then round to four decimal places)541972591440003374390914400.6157000.615765087514986000Sin 38° = Sin 52° =541972511430000337439011430000Cos 38° = Cos 52° =2623820127635Tan 38° = 00Tan 38° = 4693285141605Tan 52° =00Tan 52° =541972512763500338201012763500Part 6- Warm-UpGiven the following right triangle, write the trig ratios in fraction form.34290012954000Sin P = Sin Q = Cos P = Cos Q = Tan P = Tan Q = Part 6 – Notes: SOHCAHTOA (find missing sides)SOHCAHTOASOHCAHTOA is used to help find missing sides and angles in a right triangle when Pythagorean Theorem does not work! 43967401036300S (sine) O (opposite) H (hypotenuse) 439690211276000C (cosine) A (adjacent) H (hypotenuse) 439674015473700T (tangent) O (opposite) A (adjacent) Setting up Trigonometry Ratios and Solving for Sides_____________________________ (NOT the right angle)_____________________________ (Opposite, Adjacent, Hypotenuse)_____________________________:________ if we have the opposite and hypotenuse________ if we have the adjacent and the hypotenuse________ if we have the opposite and the adjacent Set up the proportion and solve for x! Example1: Using the given acute angle, follow the steps above to find the missing side length. Using trig ratios and your graphing calculator to approximate each length to the nearest tenth. 2.3981456654803. 46037512045954. 76200011461755. 1157605420370006. 802322108268007. 410845962025Part 6 – Classwork: In Examples 1 - 13, find the value of the missing variable(s).left952600center1184900Part 7 – Notes: SOHCAHTOA (find missing angles)Setting up Trigonometry Ratios and Solving for AnglesSelect a given angle (NOT the right angle)Label your sides (Opposite, Adjacent, Hypotenuse)Decide which trig function you can use:SOH if we have the opposite and hypotenuseCAH if we have the adjacent and the hypotenuseTOA if we have the opposite and the adjacent Solve the equation … remember to use inverses!Examples: Find the measure of angle A using the inverse of all three trig functions. 1.2.Find the measure of angles A and C. 3.4.Day 7 Classwork : Find the measure of each angle indicated. Round to the nearest tenth.Honors- To the nearest tenth, find the measure of the acute angle that the given line forms with a horizontal line. Part 7 Homework ’Part 8 – Solving Right Triangles PracticeExample 1: Given the triangle below, which of the following methods could be used to solve for x, y, and/or z.-4762515303530°yx12z30°yx12zPythagorean TheoremYes or NoIf yes, which variable(s) can I solve for _________30-60-90 TriangleYes or NoIf yes, which variable(s) can I solve for _________45-45-90 TriangleYes or NoIf yes, which variable(s) can I solve for _________Right Triangle TrigonometryYes or NoIf yes, which variable(s) can I solve for _________Example 2: Given the tringle below, which of the following methods could be used to solve for x, y, and/or z14591566486yzx162000yzx1620Pythagorean TheoremYes or NoIf yes, which variable(s) can I solve for _________30-60-90 TriangleYes or NoIf yes, which variable(s) can I solve for _________45-45-90 TriangleYes or NoIf yes, which variable(s) can I solve for _________Right Triangle TrigonometryYes or NoIf yes, which variable(s) can I solve for _________Example 3: Given the tringle below, which of the following methods could be used to solve for x, y, and/or z.28575015748057°yx12z0057°yx12zPythagorean TheoremYes or NoIf yes, which variable(s) can I solve for _________30-60-90 TriangleYes or NoIf yes, which variable(s) can I solve for _________45-45-90 TriangleYes or NoIf yes, which variable(s) can I solve for _________Right Triangle TrigonometryYes or NoIf yes, which variable(s) can I solve for _________left40005030°yx12z30°yx12zYou try #1: Solve for x, y, and z using the method of your choice.x = _______________y = _______________z = _______________left40005030°yx12z30°yx12zYou try #2: Solve for x, y, and z using a different method, formula, or strategy than you did in You Try #1.x = _______________y = _______________z = _______________What impact did your choice of method have on your final answer and the overall difficulty of the problem?__________________________________________________________________________________________________left69659500__________________________________________________________________________________________________You try #3: Solve for x, y, and z using the method of your choice.x = _______________y = _______________z = _______________You try #4: Solve for x, y, and z using the method of your choice.left16192557°yx12z0057°yx12zx = _______________y = _______________z = _______________Part 8 – ClassworkSolve for all of the missing sides and angles of the following right triangles. 1. x = __________y = __________z = __________2. x = __________y = __________z = __________3. x = __________y = __________z = __________4.x = __________y = __________z = __________5.x = __________y = __________z = __________6.x = __________y = __________z = __________7.x = __________y = __________z = __________8.x = __________y = __________z = __________Day 8 – Homework: Find all missing sides and angles in each triangle. 1. 2.3.4.5.6.7.8.Part 9 – NotesAngles of Elevation and Depression The angle of elevation is the angle formed by a __________________________ and the line of sight looking up. 2806704254500The angle of depression is the angle formed by a _______________________ and the line of sight looking down. 42672016637000Notice … the angle of elevation and the angle of depression are _____________________________ when in the same picture! 70294511620500Examples:Rachel spotted her car from a weather balloon. She knows her altitude is 82 meters and her angle of depression is 32?. She wants to know how far she is from her car.Dillon spotted his model rocket from a launch stuck in a tree. He know the base of the tree of 19 feet from the launch site. The rocket is 23 feet from the ground. He needs to calculate the angle of elevation so he can make adjustments for future launches. Round the answer to the nearest degree.You stand 40 ft from a tree. The angle of elevation from you the top of the tree is 47?. How tall is the tree?The angle of elevation to the top of a building is 22?. You know the building is 450 meters tall. How far are you from the building?Part 9 - HomeworkFor each problem draw a sketch, set up an equation and solve.1. A guy wire is attached to the top of a 75 foot tower and meets the ground at a 65? angle. How long is the wire?2. When the suns angle of elevation is 57? a building casts a shadow 21 meters long. How high is the building?3. A kite is flying at an angle of elevation of about 40?. All 80 meters of string have been let out. Ignoring the sag in the string, find the height of the kite.4. A man stands at the top of a 105 foot light house and sees a boat. The angle of depression to sight the boat is 37?, find the distance between the base of the light house and the boat.5. An observer in an airplane at a height of 500 meters sees a car at an angle of depression of 31?. If the plane is over a barn, how far is the car from the barn?6. From a point 340 meters from the base of the Hoover Dam, the angle of elevation to the top of the dam is 33?. Find the height of the dam to the nearest meter.7. The Pyramid of the Sun in the ancient Mexican city of Teotihuacan was unearthed from 1904–1910. From a point on the ground 300 feet from the center of its square base, the angle of elevation to its top would have been 31?. What was the height of the pyramid?Complete the following statements with always, sometimes, or never. 8. The tangent of an angle is ________ less than 1.9. The angle of elevation from your eye to the top of a twenty-foot flagpole ____________ gets smaller as you walk towards the flagpole.10. Given the measure of an acute angle in a right triangle and the length of one of the triangle’s legs, you can ________ use trigonometry to find the length of the hypotenuse.11. The angle of depression from the top of a building to a car traveling towards the building __________ increases as the car travels closer.Part 10 – ClassworkFind all values. Round each answer to the nearest tenth.1. Brian’s kite is flying above a field at the end of 65 m of string. If the angle of elevation to the kite measures 70°, and Brian is holding the kite 1.2 m off the ground. How high above the ground is the kite flying?2. From an airplane at an altitude (height) of 1200 m, the angle of depression to a rock on the ground measures 28°. Find the distance from the plane to the rock.3. From a point on the ground 12 ft from the base of a flagpole, the angle of elevation of the top of the pole measures 53°. How tall is the flagpole?4. From a plane flying due east at 265 m above sea level, the angles of depression of two ships sailing due east measure 35° and 25 °. How far apart are the ships?49720508890005. A man flies a kite with a 100 foot string. The angle of elevation of the string is 52?. How high off the ground is the kite?6. From the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34?. How far is the object from the base of the cliff?7. An airplane takes off 200 yards in front of a 60 foot building. At what angle of elevation must the plane take off in order to avoid crashing into the building? Assume that the airplane flies in a straight line and the angle of elevation remains constant until the airplaneflies over the building. (Don’t forget to convert the units of measure.)45045689526008. A 14 foot ladder is used to scale a 13 foot wall. At what angle of elevation must the ladder be situated in order to reach the top of the wall?9. A person stands at the window of a building so that his eyes are 12.6 m above the level ground. An object is on the ground 58.5 m away from the building on a line directly beneath the person. Compute the angle of depression of the person’s line of sight to the object on the ground.10. A ramp is needed to allow vehicles to climb a 2 foot wall. The angle of elevation in order for the vehicles to safely go up must be 30? or less, and the longest ramp available is 5 feet long. Can this ramp be used safely?Part 10- Homework- Right Triangle Word Problems Review: Draw a picture, write an equation, and solve each problem. Round measures of segments to the nearest tenth and measures of angles to the nearest degree.1. A 20-foot ladder leans against a wall so that the base of the ladder is 8 feet from the base of the building. What is the ladder’s angle of elevation?2. A 50-meter vertical tower is braced with a cable secured at the top of the tower and tied 30 meters from the base. What is the angle of depression from the top of the tower to the point on the ground where the cable is tied?1396365484505003. At a point on the ground 50 feet from the foot of a tree, the angle of elevation to the top of the tree is 53. Find the height of the tree.4. The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the sliding board?2743201012190005. Richard is flying a kite. The kite string has an angle of elevation of 60. If Richard is standing 100 feet from the point on the ground directly below the kite, find the length of the kite string.6. During a football play, DeSean Jackson runs a straight route 40 yards up the sideline before turning around and catching a pass thrown by Michael Vick. On the opposing team, a defender who started 20 yards across the field from Jackson saw the play setup and ran a slant towards Jackson. What was the distance the defender had to run to get to the spot where Jackson caught the ball?7. The perimeter of a square is 72. What is the length of the diagonal of the square?8. The angle of elevation from a car to a tower is 30. The tower is 150 ft. tall. How far is the car from the tower?9. A radio tower 200 ft. high casts a shadow 75 ft. long. What is the angle of elevation of the sun?1819275881380110 3200110 3210. An escalator from the ground floor to the second floor of a department store is 110 ft long and rises 32 ft. vertically. What is the escalator’s angle of elevation?11. The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach? 1635124840105810000810012. A ladder on a fire truck has its base 8 ft. above the ground. The maximum length of the ladder is 100 ft. If the ladder’s greatest angle of elevation possible is 70, what is the highest above the ground that it can reach?36639501584960140000140013. A person in an apartment building sights the top and bottom of an office building 500 ft. away. The angle of elevation for the top of the office building is 23 and the angle of depression for the base of the building is 50. How tall is the office building?50050014. Electronic instruments on a treasure-hunting ship detect a large object on the sea floor. The angle of depression is 29, and the instruments indicate that the direct-line distance between the ship and the object is about 1400 ft. About how far below the surface of the water is the object, and how far must the ship travel to be directly over it? ................
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