Question

A man rowing a boat away from a lighthouse which is 100 m high takes 2 min to change the angle of elevation of the light house from ${45}^{\circ }$ to ${30}^{\circ }$. Find the speed of the boat. $[Tan{45}^{\circ }=1,Tan{30}^{\circ }=0.57]$

Answer 1

Let the lighthouse $AB=100m$ and boat moves from C to D

In $△ABCTan{45}^{\circ }=\frac{100}{CB}=1\Rightarrow CB=100m$

In $△ADBTan{30}^{\circ }=\frac{100}{DB}=0.57\Rightarrow DB=\frac{100}{0.57}=175.4mCD=BD-BCCD=175.4-100=75.4\text{It takes 2 min to move from C to D}\text{Speed}=\frac{\text{Distance}}{\text{Time}}=\frac{75.4}{2}=37.7m/min$