Discussion
The angle of elevation of the top of a tower from two points P and Q at a distance of ‘a’ and ‘b’ respectively, from the base and in the same straight line with it are complementary. Prove that height
Answer: A
Let L SPR = θ then L SQR = 90º - θ and RS = h,
In Δ SPR, tan θ = h/a Or, h = a tan θ --------------------------------- (i)
In ΔSQR, tan (90º - θ) = h/b Or, h = b tan (90º - θ) = h cot θ ----- (ii)
Multiplying (i) and (ii) we get, h2 = a tan θ b cot θ = a b
Or, h = √(a b). [Proved.]
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