A statue of height 4m stands on a tower of height 10m. The angle...

A statue of height

4\text{m}

stands on a tower of height

10\text{m}.

The angle subtended by the statue at the eyes of an observer of height

2\text{m},

standing at a distance of

6\text{m}

from base of the tower is A statue of height 4m stands on a tower of height 10m. The angle subtended by the statue at the eyes of an observer of

Options

A $\tan^{- 1} \left(\dfrac{2}{11}\right)$
B $\tan^{- 1} \left(\dfrac{4}{3}\right)$
C $\tan^{-1} \left(2\right)$
D $\tan^{- 1} \left(\dfrac{7}{13}\right)$

Correct answer

A. $\tan^{- 1} \left(\dfrac{2}{11}\right)$

Step-by-step solution

From the figure
A statue of height 4m stands on a tower of height 10m. The angle subtended by the statue at the eyes of an observer of
$tan \alpha = 2, tan \beta = \dfrac{4}{3}$
$tan \theta = \dfrac{2 - \dfrac{4}{3}}{1 + \dfrac{8}{3}} = \dfrac{2}{11}$

Hence, angle subtended by the statue at the eyes of the observer is $\theta = \tan^{-1}\dfrac{2}{11}$

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