Question

If the angles of elevation of the top of a tower from the top and foot of a pole height $10mt$ are ${30}^o$ and ${60}^o$ then the height of the tower is

• A. $12mt$
• B. $15mt$
• C. $20mt$
• D. $36mt$

Answer 1

The correct option is B $15mt$

REF.Image.

In $△ABE$

$tan{60}^{\circ }=\frac{EB}{AB}$

$\sqrt{3}=\frac{10+h}{x}..\left(1\right)$

and In $△CDE$

$tan{30}^{\circ }=\frac{h}{x}$

$\frac{1}{\sqrt{3}}=\frac{h}{x},$

$x=\sqrt{3}h...\left(2\right)$

substituting x value in (1)

$\Rightarrow \sqrt{3}=\frac{10+h}{\sqrt{3}h}$

$3h=10+h$

$2h=10,h=5$

Tower's Height = BE = 10+h = 10+5 = 15

$\therefore$ Height of Tower = 15 m

option B is correct.