Question

39. A man in a boat rowing away from a lighthouse 100 m high takes
2 minutes to change the angle of elevation of the top of the light
house from 60° to 30°. Find the speed of the boat in metres per minute.
[Use 13 = 1.732.]
[CBSE 2019]​

Answer 1

Answer:

Speed of the boat:57.73

Step-by-step explanation:

Consider ΔABC

Where AB is Height of Tower 

BC is distance from boat to tower

tanC=BCAB⟹3=BC100⟹BC=57.73

Now let D be the point the boat travelled 

tanD=BDAB⟹31=BD100⟹BD=173.2

 

Distance travelled by boat CD=BD−BC=173.2−57.73=115.47m

Speed of boat=2115.47=57.73m/min