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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