Question

What is the height of a tower if the angles of elevation of its top from two points $x$ and $y$ at distance of $a$ and $b$ respectively from the base and on the same straight line with the tower, are complementary?

• A. $\frac{\sqrt{b}}{a}$
• B. $\frac{\sqrt{a}}{b}$
• C. $\sqrt{ab}$
• D. None of these

Answer 1

Answer: (C)

$\sqrt{ab}$

Let $h$ be the height of the tower $AB$
$\therefore \frac{h}{a}=tanp$.....(1)
$\frac{h}{b}=tan(90-p)=cotp$......(2)
Multiply (1) and (2), we get
$\therefore \frac{h}{a}\times \frac{h}{b}=tanp\times cotp=1$
$\Rightarrow h^2=ab\Rightarrow h=\sqrt{ab}$