Question

A boat, stationed at the North of a lighthouse, is making an angle of 30° with the top of the lighthouse. Simultaneously, another boat, stationed at the East of the same lighthouse, is making an angle of 45° with the top of the lighthouse. What will be the shortest distance between these two boats? The height of the lighthouse is 300 feet. Assume both the boats are of negligible dimensions.

Accepted Answer

D. Distance to East boat $d_1 = \frac{300}{	an 45^\circ} = 300$ feet. Distance to North boat $d_2 = \frac{300}{	an 30^\circ} = 300\sqrt{3}$ feet. Since North and East are perpendicular, distance between boats = $\sqrt{d_1^2 + d_2^2} = \sqrt{300^2 + (300\sqrt{3})^2} = \sqrt{300^2(1 + 3)} = 300 	imes 2 = 600$ feet.

Heights and Distances - 3D Trigonometry

Explanation

Practise this under exam conditions