Question

The angle of elevation of the top of the tower from two points at distance are 4m and 9m from the base of the tower and in the same straight line with it,are complementary.Find the height of the tower

Answer 1

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Answer 2

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$let \: \angle APB = \theta \\ then \angle \: AQB= ( 90 \degree - \theta) \\ in \: right \ triangle \: APB \\ \tan \theta = \frac{AB}{PB} \\ tan \theta = \frac{AB}{9}...................(1) \\ then \: in \: right \: triangle \: \: ABQ\\ tan(90 \degree - \theta) = \frac{AB}{QB} \\ cot \theta = \frac{AB}{4} ............(2) \\ multiplying \: (1)and(2) \\ \frac{AB}{9} \times \frac{AB}{4 } = tan \theta \times cot \theta \\ \frac{AB} {36}^{2} {} = 1 \\ {AB}^{2} = 36 \\ AB = \sqrt{36} \\ AB= 6m$

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