M4maths Previous Puzzles

19 Sep 2017 Distance

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 60° respectively. If the lighthouse is 189 m high, the distance between the two ships is:

OPtion

1) 416.47 m
2) 436.47 m
3) 426.47 m
4) 446.47 m
5) 466.47 m
6) 456.47 m
7) 476.47 m
8) 486.47 m
9) 496.47 m
10)None of these

Solution

Let AB be the lighthouse where A is the bottom point of light house and C and D be the positions of the ships.
Then, AB = 189 m, Angle ACB = 30° and angle ADB = 60°.
AB/AC = tan 30° = 1/sq root(3)
=> AC = AB * sq root(3) = 189*3^(1/2)

AB/AD = tan 60° = 1/sq root(3)
=> AD = AB*1/sq root(3) = 189/*3^(1/2) = 63*3^(1/2)

CD = (AC + AD) = 3^(1/2) (189+63)
= 252*3^(1/2)
= 436.47

Correct Option: 2 Best Solution (0)