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Height and Distance

Q1: 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:

A 173 m

B 200 m

C 273 m

D 300 m

ANS:A - 173 m

Let AB be the lighthouse and C and D be the positions of the ships. Then, AB = 100 m, ACB = 30° and ADB = 45°.

AB = tan 30° = 1          AC = AB x 3 = 1003 m.
AC 3
AB = tan 45° = 1          AD = AB = 100 m.
AD
 CD = (AC + AD) = (1003 + 100) m
  = 100(3 + 1)
  = (100 x 2.73) m
  = 273 m.



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