Three Angle Measure. Introduction to Trigonometry. LESSON 9.1 Assignment
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1 LESSON.1 Assignment Name Date Three Angle Measure Introduction to Trigonometry 1. Analyze triangle A and triangle DEF. Use /A and /D as the reference angles. E 7.0 cm 10.5 cm A cm D cm F a. Identify the leg opposite /A, the leg adjacent to /A, and the hypotenuse in na. b. alculate the length of the hypotenuse of triangle A. Round your answer to the nearest tenth. opposite c. alculate the ratios hypotenuse, adjacent hypotenuse, and opposite for the reference angle in triangle A. adjacent Round your answers to the nearest thousandth if necessary. hapter Assignments 15
2 LESSON.1 Assignment page 2 d. Describe the relationship between na and ndef. Eplain your reasoning. e. alculate the length of the hypotenuse in ndef without using the Pythagorean Theorem. Eplain your reasoning. opposite f. alculate the ratios hypotenuse, adjacent hypotenuse, and opposite for the reference angle in ndef. adjacent Round your answers to the nearest thousandth if necessary. g. ompare the values of the three ratios for na and ndef. What do you observe? Why do you think this is true? 160 hapter Assignments
3 LESSON.2 Assignment Name Date The Tangent Ratio Tangent Ratio, otangent Ratio, and Inverse Tangent Use the tangent ratio, the cotangent ratio, or the inverse tangent to solve for. Round each answer to the nearest tenth Z 6 cm 12 in. A 35 W 72 Y 3. R 4. J 50 m K P 23 yd 21 yd Q L 28 m hapter Assignments 161
4 LESSON.2 Assignment page 2 5. A roof truss is shown. Use the figure to complete parts (a) through (d). Round each answer to the nearest hundredth. 4 ft D A 32 H 10 ft G F E a. Determine the height G of the roof truss. b. Determine AH. c. Determine the measure of angle HG. d. Determine the length H of the support beam. 162 hapter Assignments
5 LESSON.3 Assignment Name Date The Sine Ratio Sine Ratio, osecant Ratio, and Inverse Sine Use the sine ratio, the cosecant ratio, or the inverse sine to solve for. Round each answer to the nearest tenth. 1. F 57 Y yd P S M 11 ft 25 yd 3. M 4. J 50 K 58 cm 20 cm N W 75 m hapter Assignments 163
6 LESSON.3 Assignment page 2 5. A roof truss is shown in the following figure. Use the figure to complete parts (a) through (d). Round each answer to the nearest hundredth. 16 ft 6 ft D A 40 H G F E a. Determine the height G of the roof truss. b. Determine A. c. Determine the measure of angle G. d. Determine the length G of the support beam. 164 hapter Assignments
7 LESSON.4 Assignment Name Date The osine Ratio osine Ratio, Secant Ratio, and Inverse osine Use the cosine ratio, the secant ratio, or the inverse cosine to solve for. Round each answer to the nearest tenth. 1. R 15 m 33 S in. N P T 1 in. Q 3. V 17 ft W 4. K 60 mm 22 ft J 70 F Z hapter Assignments 165
8 LESSON.4 Assignment page 2 5. A bridge is shown in the following figure. Use the figure and the fact that nag is congruent to neg to complete parts (a) through (e). Round each answer to the nearest tenth. 40 ft 27 D A ft H G F E a. Determine the width AE of the bridge. b. Determine the height G of the bridge. c. Determine H. 166 hapter Assignments
9 LESSON.4 Assignment page 3 Name Date d. Determine the measure of /H. e. Does H bisect /AG? Eplain your reasoning. hapter Assignments 167
10 168 hapter Assignments
11 LESSON.5 Assignment Name Date We omplement Each Other! omplement Angle Relationships 1. An aircraft uses its radar to locate another aircraft that is 8000 feet away at a 12 angle of depression. a. Draw a figure to model this situation. Label the angle of depression and the hypotenuse. Label the side adjacent to the angle of depression as and the side opposite the angle of depression as y. b. alculate the vertical distance between the two aircraft. Round the distance to the nearest tenth. c. alculate the horizontal distance between the two aircraft. Round the distance to the nearest tenth. hapter Assignments 16
12 LESSON.5 Assignment page 2 2. A pilot and co-pilot are performing a test run in a new airplane. The pilot is required to take off and fly in a straight path at an angle of elevation that is between 33 and 35 degrees until the plane reaches an altitude of 10,000 feet. When the plane reaches 10,000 feet, the co-pilot will take over. a. Draw a figure to model this situation. Label the angle of elevation and the side opposite the angle of elevation. Label the side adjacent to the angle of elevation as and the hypotenuse as y. b. Determine the minimum and maimum horizontal distance between the point of take-off and the point at which the co-pilot takes over. Round each distance to the nearest tenth. c. What is the minimum distance that the pilot flies the plane? What is the maimum distance that the pilot flies the plane? Round each distance to the nearest tenth. 170 hapter Assignments
13 LESSON.6 Assignment Name Date Time to Derive! Deriving the Triangle Area Formula, the Law of Sines, and the Law of osines 1. Emily and Joe are designing a fenced backyard play space for their children Ma and aroline. They start out by considering two designs for a triangular play space. They have made measurements in their yard and determined that either design would fit into the space that is available. Emily s Design Joe s Design A A 8 ft ft 8 ft ft a. Eplain how Emily and Joe can use trigonometry to calculate the area and perimeter of the possible play spaces. b. alculate the area of the play space for each design. hapter Assignments 171
14 LESSON.6 Assignment page 2 c. alculate the perimeter of the play space for each design. d. Which design do you think Emily and Joe should choose? Eplain your reasoning. 2. Emily s brother-in-law hris is an architect. She has asked him to design the placement of the playground equipment in her children s new play space. He sent her a diagram of the play space with the measurements shown. 85 A 11 ft 42 a. Eplain how Emily can calculate the area and perimeter of the play space in hris s design. 172 hapter Assignments
15 LESSON.6 Assignment page 3 Name Date b. alculate the area of the play space for hris s design. c. alculate the perimeter of the play space for hris s design. hapter Assignments 173
16 174 hapter Assignments
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