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Question
From the top of a lighthouse, 100 m high the angles of depression of two ships on opposite sides of it are 48° and 36° respectively. Find the distance between the two ships to the nearest metre.
Solution
From right angle Δ ADC,
`(AD)/(CD) = tan 36^@`
`=>100/y = tan 36^@`
`=> 100/tan 36^@ = 100/0.7265 => y = 137.638 m`
From right angle Δ ADB
`100/x = tan 48^@ => x = 100/1.1106 = 90.04 m`
∴ Distance between the ships = x + y
= 137.638 + 90.04 = 227.678 m
= 228 m (approx)
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