Question

If two towers of height $h_{1}and{h}_2$ subtend angles ${45}^{\circ }and{30}^{\circ }$ respectively at the midpoint of the line joining their feet, then find the ratio of

$h_1:h_2.$

• A. $1:2$
• B. $3:2$
• C. $\sqrt{3}:1$
• D. $1:\sqrt{3}$

Answer 1

The correct option is C

$\sqrt{3}:1$

$tan{45}^{\circ }=\frac{h_1}{x}....\left(1\right)tan{30}^{\circ }=\frac{h_2}{x}....\left(2\right)\Rightarrow \frac{tan{45}^{\circ }}{tan{30}^{\circ }}=\frac{\frac{h_1}{x}}{\frac{h_2}{x}}{h}_1:h_2=\sqrt{3}:1$