20 Chapter 1 • Right Triangle Trigonometry §1.3 Exercises 150 h 12 ◦ 34 ◦ 1. From a position 150 ft above the ground, an observer in a build-ing measures angles of depression of 12 ◦ and 34 ◦ to the top and bottom, respectively, of a smaller building, as in the picture on the right. Use this to ±nd the height h of the smaller building. h b a β α 2. Generalize Example 1.12: A person standing a ft from the base of a mountain measures an angle of elevation α from the ground to the top of the mountain. The person then walks b ft straight back and measures an angle of elevation β to the top of the mountain, as in the picture on the right. Assuming the ground is level, ±nd a formula for the height h of the mountain in terms of a , b , α , and β . 3. As the angle of elevation from the top of a tower to the sun decreases from 64 ◦ to 49 ◦ during the day, the length of the shadow of the tower increases by 92 ft along the ground. Assuming the ground is level, ±nd the height of the tower.
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