Question

On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, find the distance between the objects.

Answer 1

Let AB be the tower of height 150 m and Two objects are located when the top of the tower are observed, makes an angle of depression from the top and bottom of the tower are 45° 60° respectively.

Let CD = x, BD = y, ∠ADB = 60°, ∠ACB = 45°

So we use trigonometric ratios.

In a triangle ABC,

`tan 45^@ = 150/(x + y)`

`=> x = y = 150`   ......(1)

Again in a triangle ABD,

`tan 60^@ = 150/y`

`=> sqrt3 = 150/y`

`=> sqrt3 = 150`  ......(2)

So from (1) and (2) we get

`x + 150/sqrt3 = 150`

`=> sqrt3x = 150(sqrt3 - 1)`

`=> x = 63.39`

Hence the required distance is approximately 63.4 m