Let A and B be two towers with the same base. From the mid point of the line joining their feet, the angles of elevation of the tops of A and B are 30° and 45° respectively. The ratio of the heights of A and B is:

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& \tan 30^{\circ }=\frac{h_A}{x}\\ & h_A=\frac{1}{\sqrt{3}}x\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\left(\text{i}\right)\\ & h_B=x\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\left(\text{ii}\right)\\ & \frac{h_A}{h_B}=\frac{1}{\sqrt{3}}\end{array}$$