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From the top of a lighthouse …

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From the top of a lighthouse the angles of depression of two ships on the opposite side of it are observed to be alpha and beta. If the height of the lighthouse be h meters and the line joining the ships passes through the foot of the lighthouse show that the distance between the ship is h(tan alpha + tan beta) /tan alpha tan beta meters

Posted by Gopika Satheesh 4 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 4 years, 11 months ago

Let AD be the lighthouse whose height is h metres. 13 and C are the position of two ships which are on opposite sides of lighthouse. The angles of depression of two ships B and C from the top of the lighthouse are α and β respectively.

i.e.,    ∠ABD = α and ∠ACD = β
Let    BD = x m and CD = y m
In right triangle ABD, we jave

In right triangle ACD, we have

Adding (i) and (ii), we get

Hence, the distance between the ship is  metres.

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