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2/23/2016 Five-Minute Check (over Lesson 8–4) CCSS Then/Now New Vocabulary Example 1: Angle of Elevation Example 2: Angle of Depression Example 3: Use Two Angles of Elevation or Depression 1 2/23/2016 Over Lesson 8–4 Use a calculator to find tan 54°. Find m∠ ∠B to the nearest tenth of a degree if cos B = 0.8926 and ∠B is an acute angle. (3-4) Find x. Round to the nearest tenth. Use a special right triangle to express sin 45°as a fraction. Over Lesson 8–4 Use a calculator to find tan 54°. A. 0.6738 B. 0.7432 C. 0.8090 D. 1.3764 2 2/23/2016 Over Lesson 8–4 Find m∠ ∠B to the nearest tenth of a degree if cos B = 0.8926 and ∠B is an acute angle. A. 63.2 B. 26.8 C. 18.4 D. 0.999 Over Lesson 8–4 Find x. Round to the nearest tenth. A. 14.1 B. 17.4 C. 19.4 D. 21.3 3 2/23/2016 Over Lesson 8–4 Find x. Round to the nearest tenth. A. 9.5 B. 15.9 C. 23.7 D. 30.8 Over Lesson 8–4 Find x. Round to the nearest tenth. A. 34.7 B. 43.8 C. 46.2 D. 52.5 4 2/23/2016 Over Lesson 8–4 Use a special right triangle to express sin 45°as a fraction. A. B. C. D. Content Standards G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Mathematical Practices 4 Model with mathematics. 1 Make sense of problems and persevere in solving them. 5 2/23/2016 You used similar triangles to measure distances indirectly. • Solve problems involving angles of elevation and depression. • Use angles of elevation and depression to find the distance between two objects. • angle of elevation • angle of depression ɵ Angle of elevation ɵ Angle of depression 6 2/23/2016 Angle of Elevation CIRCUS ACTS At the circus, a person in the audience at ground level watches the high-wire routine. A 5-foot-6-inch tall acrobat is standing on a platform that is 25 feet off the ground. How far is the audience member (nearest tenth) from the base of the platform, if the angle of elevation from the audience member’s line of sight to the top of the acrobat is 27°? tan = 25 + 5.5 30.5 = ≈ 59.9 tan 27 tan 27 = DIVING At a diving competition, a 6-foot-tall diver stands atop the 32-foot platform. The front edge of the platform projects 5 feet beyond the ends of the pool. The pool itself is 50 feet in length. A camera is set up at the opposite end of the pool even with the pool’s edge. If the camera is angled so that its line of sight extends to the top of the diver’s head, what is the camera’s angle of elevation to the nearest degree? A. 37° B. 35° C. 40° D. 50° 7 2/23/2016 Angle of Depression DISTANCE Maria is at the top of a cliff and sees a seal in the water. If the cliff is 40 feet above the water and the angle of depression is 52°, what is the horizontal distance from the seal to the cliff, to the nearest foot? Notice: ∠ ≅ ∠! by AIAT tan = 40 40 = ≈ 31 tan 52 tan 52 = Kathy is in a hot air balloon 30 feet above the ground. She sees the landing spot at an angle of depression of 34°°. What is the horizontal distance between the hot air balloon and the landing spot to the nearest foot? A. 19 ft B. 20 ft C. 44 ft D. 58 ft 8 2/23/2016 9