The Angle of Elevation of the Top of a Hill at the Foot of a Tower is 60° and the Angle of Elevation of the Top of the Tower from the Foot of the Hill is 30°. If Height of the Tower is 50 M, Find the Height of the Hill. - Mathematics

The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If height of the tower is 50 m, find the height of the hill.

Solution

Let AB be the tower and CD be the hill

In ΔABD

tan 30^@ = (AB)/(BD)

=> 1/sqrt3 = 50/(BD)

=> BD = 50sqrt3

In ΔCDB

tan 60^@ = (CD)/(BD)

=> sqrt3 = (CD)/(50sqrt3)

=> CD = 150

Therefore, the height of the hill is 150 m

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 12 Trigonometry
Exercise 12.1 | Q 59 | Page 33