Question

from the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34 degrees. How far is the object from the base of the cliff.

Answer 1

From the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34 degrees. How far is the object from the base of the cliff.

Answer 2

Object is 59.30m away from the base of the cliff

Explanation:

In the figure attached, AB is a vertical cliff 40 m high, and the angle of depression is 34° of an object at the point O.

Since angle of depression is always equal to the angle of the elevation of the cliff from the object.

From Δ ABO,

tan34° =
`(AB)/(BO)`

0.6745 =
`(40)/(BO)`

BO×0.6745 = 40

BO =
`(40)/(0.6745)`

BO = 59.30 m

Therefore, object is 59.30m away from the base of the cliff .