Question

A bird on top of a 200 ft bridge tower sees a man standing on the lower part of the bridge (which is 50 ft above the ground). The angle of depression from the bird is 26 ̊. How far is the man from the base of the bridge tower? With explanation and pictures please.

Answer 1

73.2 ft is the man from the base of the bridge tower.

Explanation:

By using the trignometric property

`tan\theta = (Perpendicular)/(Base)`

As given

A bird on top of a 200 ft bridge tower sees a man standing on the lower part of the bridge (which is 50 ft above the ground).

The angle of depression from the bird is 26 ̊.

`\theta = 26^(\circ)`

Base = Height of bridge tower - Height of man

AB = AC - DE

= 200 ft - 50 ft

= 150 ft

BE = Perpendicular

Putting all the values in the trignometric property

`tan26^(\circ) = (BE)/(AB)`

`tan26^(\circ) = (BE)/(150)`

`tan26^(\circ) = 0.488\ (Approx)`

BE = 150 × 0.488

BE = 73.2 ft

Therefore 73.2 ft is the man from the base of the bridge tower.