Question 3 The angle of elevation of the top of a tower from a certain point is 30∘. If the observer moves 20m towards the tower, the angle of elevation of the top increases by 15∘. Find the height of the tower.
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Solution
Let the height of the tower be h.
Also, SR = x m, ∠PSR=θ
Given that, QS=20m
And, ∠PQR=30∘
Now, in ΔPSR,
tanθ=PRSR=hx
⇒tanθ=hx
⇒x=htanθ ...(i)
Now, in ΔPQR,
tan30∘=PRQR=PRQS+SR
⇒tan30∘=h20+x
⇒20+x=htan30∘
⇒20+x=h√3
⇒20+htanθ=h√3……(ii) [from Eq.(i)]
After moving 20 m towards the tower, the angle of elevation of the top increases by 15∘.