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° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

Question

Let AB be the lighthouse and C and D be the positions of the ships.Then, AB = 100 m,ACB = 30° andADB = 45°.AB= tan 30° =1AC = AB x3= 1003m.AC3AB= tan 45° = 1AD = AB = 100 m.ADCD = (AC + AD)= (1003+ 100) m= 100(3+ 1)= (100 x 2.73) m= 273 m.

Accepted Answer

200 m

Answer

173 m

Answer

273 m

Answer

300 m

Question 159: 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° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is: