Q. 41 A3.7( 3 Votes )

From an aeroplane, the angles of depression of two ships in a river on left and right of it are 60° and 45° respectively. If the distance between the two ships is 100m, find the height of the aeroplane.

Answer :


In right Δ ABP, we have




…(i)


In the right Δ ABQ, we have




100 – x = h


100 = h + x


[from (i)]




Multiplying and divide by the conjugate of √3 + 1, we get



[ (a – b)(a + b) = (a2 – b2)]



h = 50 (3 - √3)


h = 50 (3 – 1.732) [ √3 = 1.732]


h = 50 (1.268)


h = 63.4 m


Hence, the height of the aeroplane is 63.4m


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