Question

Determine the height of a post if the distance of the post from two points on the same side of the post are `m' and `n' metres and the angles of elevation from those points are complementary.

• A. √(m/n)metres
• B. √m metres
• C. √n metres
• D. n√m metres
• E. √mn metres

Answer 1

The correct option is E

√mn metres

Let AB be the post. Let C and D be two points at distances `m' and `n' respectively from the base of the post. Then, AC = m and AD = n. Let $\angle$ACB = $\theta$ and $\angle$ADB = 90${}^0$ - $\theta$

Let `h' be the height of the tower AB.

In $\Delta$ CAB, we have -

tan $\theta$ = $\frac{AB}{AC}$

$\Rightarrow$tan $\theta$ = $\frac{h}{m}$

In $\Delta$ DAB, we have

tan (90${}^0$ - $\theta$) = $\frac{AB}{AD}$

$\Rightarrow$ cot $\theta$ =$\frac{h}{n}$

From (i) and (ii), we have -

tan $\theta$ $\times$ cot $\theta$ = $\frac{h^2}{mn}$

$\Rightarrow$ 1= $\frac{h^2}{mn}\Rightarrow h^2=mn\Rightarrow h=\sqrt{mn}$metres

Hence, the height of the tower is $\sqrt{mn}$ metres.