Anthony B. answered • 11/10/15

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1. the angle of elevation formed by the ground and the bottom of the antenna is 62.6°

2. the side opposite to this angle is 1000

3. to find the distance from the building to the point of observation, we do: tan(62.6°) = 1000/a

4. a = 1000/tan(62.6°) ≈ 518.351

5. the angle of elevation formed by the ground and the top of the antenna is 65.8°

6. the side opposite to this angle is 1000 + the height of the antenna

7. to find this combined height, we do: tan(65.8°) = o/518.351

8. o = 518.351*tan(65.8°) ≈ 1153.383

9. now, let y = the height of the antenna

10. therefore, the height of the building + the height of the antenna = 1000 + y = 1153.383

11. subtract 1000 from both sides: y = 153.383

12. thus, the height of the antenna is approx. 153 ft