Question

The angles of elevation of the top of a vertical tower from points at distance $a$ and $b$ from the base and in the same line with it are complementary. If $a>b$, find the height of the tower.

• A. $\sqrt{ab}$
• B. $\sqrt{(a+b)}$
• C. $\sqrt{\left(a/b\right)}$
• D. $\sqrt{(b-a)}$

Answer 1

The correct option is A $\sqrt{ab}$

Let the the height of the base be $=h$

and the angle of elevation be A and B

Now, $\tan A=\frac{h}{a}tanB=\frac{h}{b}$

as the angles A and B are complimentary

$A+B={90}^o\Rightarrow A={90}^o-B\tan A=\tan ({90}^o-B)\Rightarrow \tan A=\cot B\Rightarrow \frac{h}{a}=\frac{b}{h}\Rightarrow h^2=ab\Rightarrow h=\sqrt{ab}$

Therefore, Answer is $\sqrt{ab}$