Question

The height of a tower is half the height of the flagstaff at its top. The angle of elevation of the top of the tower as seen from a distance of $10$ metres from its foot is ${30}^o$. Find the angle of elevation of the top of the flagstaff from the same point.

• A. Angle of elevation is ${35}^o$
• B. Angle of elevation is ${52}^o$
• C. Angle of elevation is ${55}^o$
• D. Angle of elevation is ${60}^o$

Answer 1

The correct option is D Angle of elevation is ${60}^o$

Let $BC$ be the flagstaff whose height is $2h$ metres. i.e., $BC=2h$metres.
By the condition of the problem, we have;
Height of the tower$=$ half the height of flagstaff
$=\frac{1}{2}2h=h$ metres.
$BAD$ is right $△$ at $A$
$\frac{AB}{BD}=\tan {30}^o$
$\frac{h}{10}=\frac{1}{\sqrt{3}}.....\left(1\right)$
$CAD$ is right $△$ at $A$
$\frac{AC}{AD}=\tan \theta$
$\frac{3h}{10}=\tan \theta ......\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$, we have
$h=\frac{10}{\sqrt{3}};h=\frac{10}{3}\tan \theta$
$\Rightarrow$ $\tan \theta =\sqrt{3}$
$\Rightarrow$ $\tan \theta =\sqrt{3}=\tan {60}^o$
$\Rightarrow$ $\theta ={60}^o$