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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°`
y = `100/tan 36°`
y = `100/(0.7265)`
y = 137.646 m
From right angle Δ ADB,
`100/x = tan 48°`
`x = 100/1.1106`
x = 90.04 m
Distance between the ships = x + y
= 137.638 + 90.04
= 227.678 m
= 228 m (appro.)
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