Question

A vertical lamp post 10 meter high stands at the corner of a rectangular field. The angle elevation of its top from the farther corner is $\frac{\pi }{6}$, while from the other corner it is $\frac{\pi }{4}$. The area of the field is.

• A. 9$\sqrt{3}$ $m^2$
• B. 100$\sqrt{3}$ $m^2$
• C. 90$\sqrt{3}$ $m^2$
• D. None of these

Answer 1

Answer: (B)

100$\sqrt{3}$ $m^2$

Let angle of elevation from A be $\frac{\pi }{6}$& B be $\frac{\pi }{4}$

Let the height of tenner be $h$ towers

so tan$\frac{\pi }{6}=\frac{h}{AB},tan\frac{\pi }{4}=\frac{h}{BC}$

$AB=h\sqrt{3};BC=h$

$Area=AB\times BC$

$=h^2\sqrt{3}$ [h=10m, given]

$=100\sqrt{3}{m}^2$