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.

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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