Two ships are sailing in the sea on the two sides of a lighthouse The angle of elevation of the top ......

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30 degree and 45 degree respectively. If the lighthouse is 100 m high, the distance between the two ships is:

Let AB be the lighthouse and C and D be the positions of the ships.
AB = 100m,∠ACB=30°,
∠ADB=45°
AB/AC=tan30=1/√3
=>AC=AB∗√3=100√3m
AB/AD=tan45
=>AB=AD=100m
CD=AC+AD
=(100√3+100)
=100(√3+1)=273m

By: MIRZA SADDAM HUSSAIN