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Question:

On a straight line passing through the foot of the tower, two points C and D are at distances of 4m and 16m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower.

Solution:

LetABbe the tower of heighth.BC=4m,BD=16m∠C=Qand∠D=90−θ.In△ABC, we havetanC=h4.. (1)And in△ABD,tanD=h16.. (2)Substituting value of equation (1) in (2), we get4tanc16=tanD⇒tanQ4=tan(90−θ).⇒tanθ=4cotθ⇒h4=4.4h... [from (1)]⇒h2=4×4×4⇒h=2×2×2⇒h=8m