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A boy 1.54 m tall can just see the sun over a wall 3.64 m high which is 2.1 m away from him. Find the angle of elevation of the sun.

Heights & Distances

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Answer

Let AD be man, BC be tower and θ be the angle of elevation.

A boy 1.54 m tall can just see the sun over a wall 3.64 m high which is 2.1 m away from him. Find the angle of elevation of the sun. Heights and Distances, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

From figure,

ABED is a rectangle.

BE = AD = 1.54 m
DE = AB = 2.1 m.

CE = BC - BE = (3.64 - 1.54) = 2.1 m.

Considering right angled triangle △DCE,

⇒tan θ=CEDE⇒tan θ=2.12.1⇒tan θ=1⇒tan θ=tan 45°⇒θ=45°\Rightarrow \text{tan θ} = \dfrac{CE}{DE} \\[1em] \Rightarrow \text{tan θ} = \dfrac{2.1}{2.1} \\[1em] \Rightarrow \text{tan θ} = 1 \\[1em] \Rightarrow \text{tan θ} = \text{tan 45°} \\[1em] \Rightarrow θ = 45°

Hence, the angle of elevation is 45°.

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