Question

The angles of elevation of the top of a tower observed from two points on the ground are ${30}^o$ and ${45}^o$. If the distance between the two points is $20$metres, then the height of the tower is

• A. $27.3m$
• B. $17.3m$
• C. $54.6$m
• D. None

Answer 1

Answer: (A)

$27.3m$

Let the height of the tower be $y$

In $△APB$

$\tan {30}^0\frac{y}{x+20}$....{i}

In $△AQB$

$\tan {45}^0=\frac{y}{x}$

$=>x=y$...................................{ii}

Putting the value of $x$ in {i} we get,

$\frac{1}{\sqrt{3}}=\frac{y}{y+20}$

$=>y+20=\sqrt{3}y$

$=>y=\frac{20}{\sqrt{3}-1}$

$=>y=\frac{20}{0.732}$ [since $\sqrt{3}=1.732$]

$=>y=27.3$m