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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
Answer & Solution
Correct Answer:
Option
D
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
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
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