From the top of hill 240 m high, the measure of the angles of depression of the top and bottom of minaret are 30° and 60° respectively. Find the height of minaret?

160 m

150 m

155 m

None of these

Given:

Height of the hill = 240 m

Angle of depression to the top of the minaret = 30°

Angle of depression to the bottom of the minaret = 60°

Let's denote the distance from the base of the hill to the minaret as x.

For the bottom of the minaret (60° angle):

tan(60°) = 240 / x

√3 = 240 / x

x = 240 / √3

For the top of the minaret (30° angle):

tan(30°) = (240 - h) / x

1/√3 = (240 - h) / (240 / √3)

Simplifying:

240 - h = 240 / 3

240 - h = 80

h = 160