Question

A vertical lamp foot of height $10$m stands at the corner of the rectangular field. The angle of elevation of its top from the farthest corner is ${30}^{\circ }$ while from one of the other two corners it is ${45}^{\circ }$, then the area of the field is

• A. $10\sqrt{3}{m}^2$
• B. $10\sqrt{2}{m}^2$
• C. $100\sqrt{2}{m}^2$
• D. $100\sqrt{3}{m}^2$

Answer 1

The correct option is C $100\sqrt{2}{m}^2$

Angle is ${45}^{\circ }$ so one side is of $10$m
let other side be $x$
$\frac{10}{\sqrt{{10}^2+x^2}}=\tan {30}^{\circ }$
$x=10\sqrt{2}$
Area = $100\sqrt{2}{m}^2$