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An idol 30m tall stands on a pillar 15 m high. What will be the angle in degrees which the idol subtends at a point of distance $153 m$ from the base of the pillar?

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20 °

40 °

30 °

50 °

answer is C.

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Detailed Solution

Given that,
The height of the idol

A B = 30

m
The height of the pillar

B D = 15

m The distance from the base of the pillar

D E = 153

m
We construct a schematic diagram,
Question Image

AB = the height of the idol
BD =the height of the pillar.
By the tangent rule in the right-angle triangle

Δ A D E

tan θ = Height Base ⇒ tan θ = D E A D

The total height of the idol and pillar can be written as,

A D = 30 + 15 ⇒ A D = 45

Substituting DE=

153

and AD=45 in

tan θ = D E A D

⇒ tan θ = 153 30 + 15 ⇒ tan θ = 15345 ⇒ tan θ = 13

⇒ θ = tan − 1 13 ⇒ θ = 30 °

Thus the angle in degree is

30 °

.
Therefore the correct option is 3.

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