Unit 3



centercenterGSE GEOMETRYpEBBLEBROOK HIGH SCHOOL | mATH DEPARTMENTUnit 3Right Triangles trigonometry8820090900GSE GEOMETRYpEBBLEBROOK HIGH SCHOOL | mATH DEPARTMENTUnit 3Right Triangles trigonometryVocabulary BuilderChoose the concept from the list below that best represents the item in each box.Draw a line from each word in Column A to its definition in Column B.293370069850029718001765300010. Sine29813251244600011. Cosine3009900914400012. Tangent3000375251460003000375198755003 - 1 Trigonometric RatiosIf the ____________________________ of a number is a whole number, the original number is called a __________________________________, which is a number multiplied by itself.35547308128000A _______________________________________________ is an expression that contains a square root. The number under the radical sign is called the __________________________________.To simplify a radical expression, make sure that the radicand has no __________________________ factors other than 1.Example 1Simplify each expression.Simplify each expression.3409950000The Pythagorean Theorem is probably the most famous mathematical relationship. The theorem states that in a ______________________________, the sum of the squares of the lengths of the legs _________________ the square of the length of the ___________________________________.The Pythagorean Theorem given you a way to find unknown ____________________________ when you know a triangle is a right triangle.Example 2Find the value of x. Give your answer in simplest radical form. Find the value of x. Give your answer in simplest radical form.401002569850020097758318500 34194756667500We will further study right triangles by looking at trigonometric values as defined by ratios of the sides of a right triangle. The side labeled ________________________ is always opposite the right angle of the right triangle. The other two sides of the right triangle are determined by the angle that is being discussed. The __________________________ side will always make up part of the angle that is being discussed and cannot be the hypotenuse. The side of the right triangle that DOES NOT form part of the discussed angle is called the _______________________ side.Example 3Identify the opposite, adjacent, and hypotenuse of the following triangles.324802521018400Identify the opposite, adjacent, and hypotenuse of the following triangles. A _______________________________________ is a ratio of two sides of a right triangle. Thinking _________________can help you remember these ratios. Using the ratios below, you can find the ________________ of any side of a ________________ triangle if you know one ________________ angle and any other side.3286125685165329565089154043910256946903276600107569043815001075690326707512915904400550159956532861251567815328612517741904381500199009032670751958340327660021647153267075250126543815002512060326707526885904391025287655032670753088005032670752882265Example 3Write each trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.lefttop45720010922041529009525231457510795Write each trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. 235267527432041910008255 Simplify the square root. Write each trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.4210050635020764506350left6350 Simplify each square root in simplest radical form. Identify the sides of the right triangle below.32245301143000Find the value of each trigonometric ratio.14001755461000-19050546100046386752603500 Find the missing side of each triangle. Leave your answers in simplest radical form.3228975762000 3 - 2 Finding Missing Sides and Angles of a Right TriangleSine, Cosine, and Tangent are trigonometric __________________. The __________________ of each function is a(n) ______________________ measure. For each trigonometric function, every acute angle measure produces a different __________________________, or value of the function. Example 1Find each length. Round to the nearest hundredth.Find each missing length. Round to the nearest hundredth.Using an inverse trigonometric function, such as __________, ___________, __________ allows you to determine an unknown angle measure given sides of right triangle.Example 202470151.001.Find the missing measure. Round to the nearest tenth.4076700101603.003.204787569852.002.center6985429577554610 Find the missing measure. Round to the nearest tenth.21526501143004352925104775 0-6354.004.2047875539755.005.4076700571506.006.21050252597152.002.02311401.001.419100017468000Find each missing measure. Round to the nearest tenth.4429125419735x?x?5048250248285402907595253.003. -590552162711.001.Find each missing measure. Round to the nearest tenth.44881801960880000535413010.0010.5797534922660044057445322042002137410540048511.0011.2161309544079400-23751540516900441762135882450021375583540744002089785184169000left1942960004417621968980021613083752200left1896004417621528388412.0012.left34550857.007.440574519350436.006.212568318994175.005.left18875414.004.4381995943673.003.2077720107952.002.YYYYYY44291251711869.009.2137410962568.008.3811905296545003 – 3 Sine and Cosine of Complementary AnglesThe sum of the measures of the interior angles of a triangle is ____________. Every right triangle has one right angle, so the sum of the measures of the two acute angles in any right triangle must be equal to ___________. Angles that add up to 90? ________________________________ angles.In a right triangle, the __________________________________ for one acute angle is the adjacent leg for the other acute angle. So, the sine of one acute angle is equal to the _______________________ of its complement, and vice versa. 119887223132sinA=cos?(90-A)cosB=sin?(90-B)0sinA=cos?(90-A)cosB=sin?(90-B)Example 1Write each trigonometric function in terms of its complement.1. sin64?2. cos84?3. cos38 ?4. sin24 ?5. cos72 ?6. sin45?Write each trigonometric function in terms of its complement.1. sin22?2. cos65?3. cos44 ?4. sin32 ?5. cos25 ?6. sin15?Example 23063768353340Find the missing values.right1313089a. sinA=_______ b. sinB=_______b. cosA=_______ d. cosB=_______0a. sinA=_______ b. sinB=_______b. cosA=_______ d. cosB=_______-2709551375196a. sinA=_______ b. sinB=_______b. cosA=_______ d. cosB=_______0a. sinA=_______ b. sinB=_______b. cosA=_______ d. cosB=_______3895106598210mP = 30?0mP = 30? What do you notice about the relationship between sine and cosine?__________________________________________________________________________________________-47568307451K00K3289399227824Find the missing values. 26105341181722J00J-601441198113L00L30251401514030a. sinS=_______ b. sinT=_______b. cosS=_______ d. cosT=_______0a. sinS=_______ b. sinT=_______b. cosS=_______ d. cosT=_______-2590801517700a. sinK=_______ b. sinJ=_______b. cosK=_______ d. cosJ=_______0a. sinK=_______ b. sinJ=_______b. cosK=_______ d. cosJ=_______382385411987734203865167236mS = 45?0mS = 45?4049486300437 What do you notice about the relationship between sine and cosine?__________________________________________________________________________________________Example 3Write each trigonometric expression.Write each trigonometric expression.Example 4Draw ABC where ACB = 90?. AC = 5 and CB = 12.a. What is the length of AB?b. What is cos A?c. What is sin B?Draw HAT where H = 90? and tanA= 1235.a. What is the length of AT?b. What is sin A?c. What is cos T?Draw XYZ where Y = 90?. XY = 8 and YZ= 6.a. What is the length of XZ?b. What is cos X?c. What is sin Z?Draw MIX where I = 90? and cosX= 35.a. What is the length of IM?b. What is sin X?c. What is cos M?Write each trigonometric function in terms of its complement.1. sin13?2. cos66?3. sin75 ?1685100317500W00W-690253060704.004.Find the missing values. 1685925665925Y00Y-178129635074V00V7481468848771500156883401841501700172517569155360a. sinW=_______ b. sinV=_______b. cosW=_______ d. cosV=_______0a. sinW=_______ b. sinV=_______b. cosW=_______ d. cosV=_______ 5. Draw BAD where A= 90? and cosD= 915.a. What is the length of IM?b. What is sin D? c. What is cos B? Write each trigonometric function in terms of its complement.1. cos30?2. sin80?3. cos45 ?4. sin73?5. cos26?6. sin25 ?Find the missing values.007.007.2303813178130a. sinK=_______ b. sinL=_______b. cosK=_______ d. cosL=_______0a. sinK=_______ b. sinL=_______b. cosK=_______ d. cosL=_______left1283778.008.223256111240a. sinK=_______ b. sinL=_______b. cosK=_______ d. cosL=_______0a. sinK=_______ b. sinL=_______b. cosK=_______ d. cosL=_______9. Draw PAT where A= 90? and cosP= 45.a. What is the length of AT?b. What is sin P? c. What is cos T? 3 – 4 Solve Right TrianglesNow that we know how to write the 3 trigonometric functions of a right triangle, we can use these ratios to _______________________ a right triangle. Solving a right triangle means that we use given _________________________ and ____________________________ measures to calculate missing sides and angle measures.577969905774569343646982569343383097Example 12850742578185a. RP=_______ b. ∠P=_______c. ∠R=_______ 00a. RP=_______ b. ∠P=_______c. ∠R=_______ Find ALL the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.2415401218500001.001.2842835493203a. BC=_______ b. AB=_______c. ∠C=_______ 00a. BC=_______ b. AB=_______c. ∠C=_______ left6142962.002.Find ALL the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. A(n) ______________________________________ is the angle formed by a horizontal line and the line of sight to an object ABOVE the horizontal line. -6355435600A(n) ______________________________________is the angle formed by a horizontal line and the line of sight to an object BELOW that horizontal line. Example 2286397028754700Describe each angle as it relates to the situation in the diagram.314001525552200Describe each angle as it relates to the situation in the diagram. Example 31958053260985Find the value of x. Round to the nearest tenth.-20685418183893.003.3062378156242.002.left95131.001.332114612724 4071668223149363277524875200Find the value of x. Round to the nearest tenth.15700078626001.001. -85090575213.003. 326031827554200Describe each angle as it relates to the situation in the diagram.1173192337125-1552763664075.005.Find the value of x. Round to the nearest tenth.-11140113061957.007.302772812466258.008.24752301200905546914811341574641012127243010619218666.006.-1639022754109.009. 1104182619148 1000664286829319177269588-1207704227551.001.Find the value of x. Round to the nearest tenth.53213001579616right2744821738571606082236363710196287259616151534.004.-15527616237783.003.2863970106392.002.310528222012900Describe each angle as it relates to the situation in the diagram. -1984083445419.009.3213100439947 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download