Question

The angle of elevation of the top of a tower is ${30}^{\circ }$​. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled. State whether the given statement is true or false.

• A. True
• B. False

Answer 1

The correct option is B

False

CaseI: Let the height of the tower be h and BC = x m

$tan{30}^{\circ }=\frac{AC}{BC}=\frac{h}{x}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{x}$------ (i)

Case II By condition, the height of the tower is doubled, i.e., PR = 2h.

In PQR, tan = $\frac{PR}{QR}=\frac{2h}{x}$

⇒ tan$\theta =\frac{2}{\sqrt{3}}$ = 1.15 [Substitute h from equation(i)]

$\theta$ = $ta{n}^{-1}$(1.15) < ${60}^{\circ }$

Hence, the required angle is not doubled.

So, the given statement is false.