Question : From two points on the ground lying in a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distance of the two points from the foot of the pillar are 9 m and 16 m and the two points lie on the same side of the pillar, then the height of the pillar is:
Option 1: 5 m
Option 2: 10 m
Option 3: 7 m
Option 4: 12 m
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Correct Answer: 12 m
Solution : Let $AB$ be the height of the pole. $BC$ = 9 m and $BD$ = 16 m $\angle ADB = \theta$ $\angle ACB = 90°-\theta$ From $\triangle ABC$, $\tan (90°-\theta) = \frac{AB}{BC}$ ⇒ $\cot$ $\theta$ = $\frac{AB}{9}$------------------(i) From $\triangle$ABD, $\tan$ $\theta$ = $\frac{AB}{16}$----------------(ii) Multiplying equations (i) and (ii), $AB^2$ = 144 ⇒ $AB$ = 12 m Hence, the correct answer is 12 m.
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