#6 Half angle identities (in image) In this module you have worked with many different trigonometrie identities. These identitiescan be helpful for making precise calculations. For example, you can use identities to find thelengths of the sides of a triangle when the angle measure in standard position is not listed on theunit circle.Most recently you have learmed about double-angle and half-angle identities. These are specialcases of the sum and difference formulas for sine and cosine.Consider the half-angle identities shown as you work through the scenario below.Sine Half-Angle IdentityCosine Half-Angle Identity1- cose1+ cosesin = +cos=Marcus is a craftsman and artist. He uses theknowledge he has gained as an engineering student tocreate custom pieces. For his current oroiect. he ismaking a large, intricate, 3-dimensional latticeworkthat will be placed next to the marker which wekomespeople to his city. He has the work on the latticecompleted. It consists of two long rectangles, such thatthe bottom rectangle will act as a base for the toprectangle. Together the two rectangles are 12 feet tall,12 ftIn order to help the latticework remain vertical, Marcuswill attach two wires to cach side of the piece, and affixthem to the ground at a point that is exactly 9 feet from thebase of the artwork, as shown in the illustration. Themeasure of the angle of elevation to the top of the base isone-half the measure of the angle of elevation to the top ofthe latticework.Use this information and what you know abouttrigonometric ratios and identities to help you explore thequestions below.9ft1. Can you use the given information to calculate the measure of the angle of elevation to the topTthe latticework? If so. find the anele measure to the nearest degree. Show your work. If not,explain why not and what information is Teeded.2. What length of wire will Marcus need to attach the top of the latticework to the ground? Showyour work.3. Can vou use the given information to find the exact heicht of the base? If so, find the heightand show your work. If not, explain why not and what information is needed.t4. Consider your responses to question 3. Devise a plan to find any information that you need inorder to find the height of the base.5. Carry out your plan from question 4 and state the height of cach rectangle.6. How much wire will Marcus need to secure his latticework to the ground? Round to thenearest foot and explain how you found your answers.

It is given that, Angle of elevation of top of base region is =θ2 Angle of elevation of top of…

can be helpful for making precise calculations. For example, you can use identities to find the lengths of the sides of a triangle when the angle measure in standard position is not listed on the unit circle. Most recently you have leamed about double-angle and half-angle identities. These are special cases of the sum and difference formulas for sine and cosine. Consider the half-angle identities shown as you work through the scenario below. Sine Half-Angle Identity Cosine Half-Angle Identity 1- cose 1+ cose sin -+ cos- Marcus is a craftsman and artist. He uses the knowledge he has gained as an engineering student to create custom pieces. For his current proiect. he is king za large, intricate, 3-dimensional latticework that will be placed next to the marker which wekomes people to his city. He has the work on the lattice completed. It consists of two long rectangles, such that the bottom rectanele will act as a base for the top rectangle. Together the two rectangles are 12 feet tall. In order to help the latticework remain vertical, Marcus will attach two wires to each side of the piece, and affix them to the ground at a point that is exactly 9 feet from the base of the artwork, as shown in the illustration. The measure of the angle of elevation to the top of the base is 12t one-half the measure of the angle of elevation to the top of the latticework. Use this information and what you know about trigonometric ratios and identities to help you explore the questions below. 9 ft 1. Can you use the given information to calculate the measure of the angle of elevation to the top of the latticework? If so. find the anele measure to the nearest degree. Show your work. If not, explain why not and what information is needed. 2. What length of wire will Marcus need to attach the top of the laticework to the ground? Show your work. 3. Can vou use the eiven information to find the exact heieht of the base? If so, find the height and show your work. If not, explain why not and what information is needed. 4. Consider your responses to question 3. Devise a plan to find any information that you need in onder to find the height of the base. 5. Carry out your plan from question 4 and state the height of each rectangle. 6. How much wire will Marcus need to secure his latticework to the ground? Round to the nearest foot and explain how you found your answers.