Question

A tower $51$ mts high has a mark at a height of $25$ mts from the ground. At what distance the two parts subtend equal angle to an eye at the height of $5$ mts from the ground.

• A. $20$ mts
• B. $30$ mts
• C. $15$ mts
• D. $160$ mts

Answer 1

The correct option is D $160$ mts

$\tan \theta =\frac{5}{d}$ ..... $\left(1\right)$

$\tan (\alpha -\theta )=\frac{20}{d}$ ...... $\left(2\right)$

$\tan (2\alpha -\theta )=\frac{46}{d}$

From $\left(1\right)$ and $\left(2\right)$, we get

$\tan \alpha =\frac{25d}{d^2-100}$

$\tan (\alpha +(\alpha -\theta \left)\right)=\frac{46}{d}.$

$\frac{\frac{25d}{d^2-100}-\frac{20}{d}}{1-\frac{(25d}{d^2-100)}\times \frac{20}{d}}=\frac{46}{d}$

On solving for $d$ we can get

$d=160$