The horizontal distance between two towers is 80 m. The angle of depression of the top of the first tower when seen from the top

Question

lana66690 [7]

3 years ago

12

The horizontal distance between two towers is 80 m. The angle of depression of the top of the first tower when seen from the top

of the second tower is 30o. If the height of the second tower is 160 m, find the height of the first tower.

Mathematics

1 answer:

Yuliya22 [10] · Answer 1 · 2022-09-26T23:18:45+03:00

Yuliya22 [10]3 years ago

8 0

Let the height of the first tower be x, then the second tower is (160 - x) m taller than the first tower. Then
tan 30 = (160 - x)/80
160 - x = 80 tan 30
x = 160 - 80 tan 30 = 160 - 46.19 = 113.8 m

Therefore, the height of the first tower is 113.8 m.