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Question
As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.
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Solution
Let AB be the lighthouse and C and D be the two ships.
The angles of depression of the 2 ships are 30° and 40°
So, ∠ADB = 30°
∠ACB = 40°
Let the distance between the ships be CD = x m.
Also, Let BD = y m.
In ΔABC
`tan 40^@ = 80/(y - x)`
`=> y - x = 80/0.8390 = 95.352` ....(1)
Also from ΔABD
`tan 30^@ = 80/y`
`=> y = 80sqrt3 = 80 xx 1.732m` = 138.56 m
From (1) we get
`138.56 - x = 95.352`
`=> x = 138.56 - 95.352 cm = 43.208 m ~~ 43m`
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