Question

The angle of elevation of stationary cloud from a point 25 ml above the lake is ${15}^0$ and the angle of depression of reflection in the lake is ${45}^0$ .Then the height of the cloud above the level

• A. $25\sqrt{3}mt$
• B. $\frac{25\sqrt{3}}{3}mt$
• C. $20\sqrt{3}mt$
• D. $\frac{50\sqrt{3}}{\sqrt{3}+1}mt$

Answer 1

The correct option is D $\frac{50\sqrt{3}}{\sqrt{3}+1}mt$

$tan{15}^{\circ }=\frac{x}{25}$

$\therefore x=25tan{15}^{\circ }$

$=25\left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)$

$\therefore$ Height $=25+25\left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)$

$=\frac{50\sqrt{3}}{\sqrt{3}+1}$