Question

The angles of elevation of the top of a temple, from the foot and the top of a building $30m$ high, are ${60}^{\circ }$ and ${30}^{\circ }$ respectively. Then height of the temple is

• A. $50m$
• B. $43m$
• C. $40m$
• D. $45m$

Answer 1

Answer: (D)

$45m$

In $△DBC$,

$\tan {60}^{\circ }=\frac{x+30}{BC}$

$\Rightarrow BC=\frac{x+30}{\sqrt{3}}.....\left(1\right)$

In $△DAE$,

$\Rightarrow \tan {30}^{\circ }=\frac{DE}{AE}$

Now, $AE=BC$

$\frac{x}{\frac{x+30}{\sqrt{3}}}=\frac{1}{\sqrt{3}}$

$\Rightarrow \sqrt{3}x=\frac{x+30}{\sqrt{3}}$

$\Rightarrow 3x=x+30$

$\Rightarrow 2x=30$

$\Rightarrow x=15m$

$\therefore h=x+30$

$=15+30=45m$