From the top and bottom of a straight hill; the angle of depression and elevation of the top of a pillar of 10 m height are observed to be 60° and 30° respectively. The height (in metres) of the hill is

A. 30

B. 80

C. 60

D. 40

Answer: Option D

Solution(By Examveda Team)

According to the question

From figure, AB = CD
Height of pillar BC = AD = 10 m
In ΔABC,
AB = BC cot 30°
AB = 10√3 m
Also AB = CD = 10√3 m
In ΔCDE,
DE = DC tan 60°
DE = 10√3 √3 = 30
Height of the hill = AD + DE
= 10 + 30
= 40 m