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Unit 8: Right Triangles and TrigonometryTopic/AssignmentI CAN statementTurned in?Simplifying RadicalsHW: Radicals Worksheet1) I can recognize perfect square factors2) I can simplify radicals completelyYes NoPythagorean TheoremHW: Pythagorean Theorem Worksheet1) I can find sides of a right triangle using Pythagorean theorem2) I can use the converse to determine if a triangle is a right triangle. Yes NoSpecial Right Triangles AHW: Worksheet1) I can recognize a triangle2) I can use the pattern to find missing side lengthsYes NoSpecial Right Triangles BHW: Worksheet1) I can recognize a triangle2) I can use the pattern to find missing side lengthsYes NoMid-Unit Review and QuizMid-Unit Review SheetYes NoSine, cosine, and tangent ratiosHW: Trig Worksheet 1) I can apply the sine, cosine, and tangent ratios to find missing sides lengthsYes NoSolving TrianglesHW: Solving Triangles Worksheet1) I can apply the inverse trig functions to find missing angle measurements.2) I can solve a triangle by finding all side lengths and all angle measurements. Yes NoUnit 8 ReviewYes NoUnit 8 Test**If all eight assignments are completed by the day the Unit 8 test is given you will receive 5 extra points on the test. **Simplifying Radicals ReviewObjectives: 1) I can recognize perfect square factors2) I can simplify radicals completelySimplifying RadicalsSimplify the following radical expressions completely. 1) 7) 13) 2) 8) 14) 3) 9) 15) 4) 10) 16) 5) 11) 17) 6) 12) 18) THE PYTHAGOREAN THEOREM/CONVERSEObjectives: 1) I can find sides of a right triangle using Pythagorean Theorem.2) I can use the converse to determine if a triangle is a right triangle.Pythagorean TheoremPythagorean TripleSimplify each:A. B. C. Find the length of the missing side of the triangle. Leave answers in simplified radical form. 29718001282705257800128905A. 2286008890B. C. 2971800163195514350023495228600137795D. E. F. Find the area of the triangle to the nearest tenth of a meter.5238751473200037719003302045720019240500B. You place a 10 foot ladder against a wall. If the base of the ladder is three ft. from the wall, how high up the wall does the top of the ladder reach? Draw a sketch!Pythagorean Theorem Converse: If , then ABC is _____________.6032563500If , then ABC is _____________.70485-5715If , then ABC is _____________.6096060960Are the triangles obtuse, right, or acute?190503175034480505080a)b) 023495CAN THE SIDE LENGTHS FORM A TRIANGLE? HOW DO YOU KNOW?00CAN THE SIDE LENGTHS FORM A TRIANGLE? HOW DO YOU KNOW?Can these side lengths form a triangle? Show why or why not.a) 5, 4, 3b) 5, 5, 10c) 5, 10, 15d) 5, 10, 10If a triangle can be formed, classify each triangle as acute, obtuse, or right based on the following side lengths. FIRST: show if the 3 numbers can form a triangle. IF SO: show if it’s right obtuse or acutea) 5, 12, 13b) 6, 5, 12c) 7, 8, 9SPECIAL RIGHT TRIANGLES (A)Objectives: 1) I can recognize a triangle2) I can use the pattern to find missing side lengths5487035431800045 - 45 - 90 Triangle Theorem Fill in the table with the missing side lengths of the 45-45-90 triangle. Leave all answers in simplified radical form.Leg (x)Leg (x)Hypotenuse ()5-1556385138430xx00xx101545-45-90 Rules:When you are given the length of a LEG ________________ by to get the length of the HYPOTENUSE.When you are given the length of the HYPOTENUSE _______________ by to get the length of the LEG.Find all the missing side lengths. Leave answers in simplified radical form.37998407175545°45°0045°45°118745125095845°45°00845°45°a)b)39185851651001045°45°001045°45°2895601841545°45°60045°45°6c) d)39185852667045°45°0045°45°02667045°45°0045°45°e)f) SPECIAL RIGHT TRIANGLES (B)Objectives: 1) I can recognize a triangle2) I can use the pattern to find missing side lengths-57150698500510603549530x00x30 - 60 - 90 Triangle TheoremFill in the table with the missing side lengths of the 30-60-90 triangle. Leave all answers in simplified radical form.Short Leg (x)Long Leg ()Hypotenuse (2x)-1694815140970x2x00x2x62082718Find all the missing side lengths. 12452356667510001045853354127530°0030°5594359207560°0060°42805356667500a.b.489013514351000569023516891060°0060°16389351016030°0030°571500-5715000041662351009650036893513271560°0060°3943353111500c. d. 41281354572060°0060°63510096500145161010477530°0030°5213985952530°0030°476758066675180018TRIGONOMETRYObjectives: 1) I can apply the sine, cosine, and tangent ratios to find missing sides lengths410243119916900075565The 2 acute angles of a right triangle each have… A C B 00The 2 acute angles of a right triangle each have… A C B 42189401409700041032328898300Trigonometric Ratio: the ratio of 2 sides of a right triangle. a number has special name(s) helps find a missing side or angle of a right triangle488632582550ABC00ABCSineCosineTangentSOHCAHTOAFind the sine, cosine, and tangent of .34290084455Find the sine, cosine, and tangent of S for the first triangle and R of the second triangle. Express each value as a simplified fraction.3952875127635i) 1365250ii) SUse your calculator to find the following trig ratios (round to the nearest tenth).=B) =C) =Solve the following for the variable (round to the nearest tenth). B) C) D) E) F) Use trigonometric ratios to find the value of the variables. Round to the nearest hundredth.18923076203729990139705x27005x27A) B) 365315533655C) 241935-5080D) SOLVING RIGHT TRIANGLESObjectives: 1) I can apply the inverse trig functions to find missing angle measurements.2) I can solve a triangle by finding all side lengths and all angle measurements.RIGHT TRIANGLES HAVE:SOLVING A RIGHT MEANS:TO SOLVE, YOU MUST KNOW EITHER:*Once you know the sine, cosine, or tangent of an acute angle, you can use a calculator to find the measure of the angle.FOR ANY ACUTE ANGLE A:If sin A = x, thenIf cos A = y, thenIf tan A = z, thenIf you are finding a SIDE you use ________________________.If you are finding an ANGLE you use ______________________.Solve the following right triangles. Round decimals to the nearest tenth. 3895090167640133350100330A. B. 3436620831852374906985C. D. 4734670359Applications: 1) During its approach to Earth, the space shuttle’s glide angle changes. When the shuttle’s altitude is about 15.7 miles, its horizontal distance to the runway is about 59 miles. What is its glide angle? Round your answer to the nearest tenth. When the space shuttle is 5 miles from the runway, its glide angels is about 19. Find the shuttle’s altitude at this point in its descent. Round your answer to the nearest tenth. 4512365400381002) During a flight, a hot air balloon is observed by two persons standing at points A and B as illustrated in the diagram. The angle of elevation of point A is 28. Point A is 1.8 miles from the balloon as measure along the ground. Round answers to the nearest tenth.What is the height, h, of the balloon? Point B is 2.9 miles from point A. Find the angle of elevation of point B. ................
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