Question

The angles of elevations of the top of the tower from two points in the same straight line and at a distance of $9m$, and $16m$ from the base of the tower are complementary. The height of the tower is

• A. $18m$
• B. $16m$
• C. $10m$
• D. $12m$

Answer 1

Answer: (D)

$12m$

$\angle ADB+\angle ACB={90}^o$....(given)
$\therefore \angle ACB={90}^o-\angle ADB$
Applying tan on both the sides, we get
$\tan \left(\angle ACB\right)=\tan ({90}^o-\angle ADB)$
$\therefore \tan \left(\angle ACB\right)=\cot (\angle ADB$)
$\therefore \tan \left(\angle ACB\right)\times \tan \left(\angle ADB\right)=1$
$\therefore \frac{h}{16}\times \frac{h}{9}=1$
$\therefore h=12$
Hence, option $D$ is the correct answer.