Question

From the top of a cliff of $200mt$ height, the angle of depression of the top and bottom of tower are observed to be ${30}^o$ and ${60}^o$ respectively. Then the height of the tower is

• A. $120mt$
• B. $133.3mts$
• C. $135mts$
• D. $122.5mts$

Answer 1

The correct option is B $133.3mts$

In $\Delta ABC$,

$\begin{array}{c}\tan {60}^0=\frac{200}{BC}\\ BC=\frac{200}{\sqrt{3}}\end{array}$

In $\Delta ADE$,

$DE=BC=\frac{200}{\sqrt{3}}$

$\begin{array}{c}\tan {30}^0=\frac{AE}{DE}\\ AE=\frac{1}{\sqrt{3}}\times \frac{200}{\sqrt{3}}=\frac{200}{3}\\ AB-AE=BE\end{array}$

Height of the tower $=CD=BE$

$\begin{array}{c}=\left(200-\frac{200}{3}\right)m\\ =\frac{4000}{3}m=133.3\end{array}$

Option $B$ is correct answer.