Question

From a point P on the ground, the angle of elevation of the top of a 20 m tall building is ${30}^{\circ }$. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff is ${45}^{\circ }$. Find the height of the flag. (You may take $\sqrt{3}$ = 1.732)

• A. 20 m
• B. 14.64 m
• C. 20√3 m
• D. 10 m

Answer 1

The correct option is B

14.64 m

BC = 20 m, Let CD(Flag) = x

Then, BD = x +20

From $\Delta$ABD, AB = BD and from $\Delta$ABC, AB = BC$\sqrt{3}$

But BD = BC$\sqrt{3}$

x+ 20 = 20$\sqrt{3}$

$⟹$x = 20( $\sqrt{3}$ - 1)

x = 14.64 m

Hence, the height of the flag is 14.64 m