From the top of a $45$ m high light house, the angles of depression of two ships, on the opposite side of it, are observed to be $30°$ and $60°$. If the line joining the ships passes through the foot

Question

From the top of a $45$ m high light house, the angles of depression of two ships, on the opposite side of it, are observed to be $30°$ and $60°$. If the line joining the ships passes through the foot of the light house, find the distance between the ships. (Use $\sqrt{3} = 1.73$)

Accepted Answer

Step 1: Lighthouse AB of height 45 m with ships C and D on opposite sides, angles of depression 30 and 60 degrees
Step 2: $	an 60° = \sqrt{3} = \frac{45}{y} \Rightarrow y = \frac{45}{\sqrt{3}} = 15\sqrt{3}$
Step 3: $	an 30° = \frac{1}{\sqrt{3}} = \frac{45}{x} \Rightarrow x = 45\sqrt{3}$
Step 4: Distance between two ships $= x + y = 45\sqrt{3} + 15\sqrt{3} = 60\sqrt{3} = 60 	imes 1.73 = 103.8$ m

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