From the top of a light house the angle of incidence of the two ships are 45&30 degree respectively if both the ships are at a distance 200m from each other then find out the height of the light house
Make a sketch
Clearly the ship with the smaller angle is farther away.
Label the two ships A and B, B closer to the lighthouse.
Label the top and bottom of the lighthouse P and Q.
enter the angles and AB=200
in triangle ABP, I have
angle A = 30°
angle ABP = 135°
angle APB = 15°
AB=200
by the sine law:
BP/sin30 = 200/sin15
BP = 200sin30/sin15
= ...
Now go to the right-angled triangle BPQ,
use sin45 = PQ/BP to find PQ