Q41 of 68 Page 9

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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