Question

The angles of elevation of the top of the tower from two points in the same straight line and at a distance of $9\text{m}$ and $16\text{m}$ from the base of the tower are complementary. The height of the tower is

• A. $18\text{m}$
• B. $16\text{m}$
• C. $10\text{m}$
• D. $12\text{m}$

Answer 1

The correct option is D $12\text{m}$

In $△ABC$,

$\tan \theta =\frac{h}{9}\dots \left(i\right)$

In $△ABD$,

$\tan (90-\theta )=\frac{h}{16}$

$\Rightarrow \cot \theta =\frac{h}{16}\dots \left(ii\right)$

Multiply the equations $\left(i\right)$ and $\left(ii\right)$,

$\begin{array}{cc}\tan \theta \times \cot \theta & =\frac{h^2}{9\times 16}\\ h^2& =9\times 16\\ h& =3\times 4\\ & =12\end{array}$

So, the height of the tower is equal to $12\text{m}$.