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Height and Distance
Height and Distance
Easy

Question

Consider a triangular plot ABC with sides AB = 7m, BC = 5m and CA = 6m. A vertical lamp-post at the mid point D of AC subtends an angle 30 o at B. The height (in m) of the lamp-post is -

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Solution

BD = hcot30 o = h3\sqrt 3 So, 7 2 + 5 2 = 2(h3\sqrt 3 ) 2 + 3 2 ) ⇒\Rightarrow 37 = 3h 2 + 9 ⇒\Rightarrow 3h 2 = 28 ⇒\Rightarrow h = 283=2321\sqrt {{{28} \over 3}} = {2 \over 3}\sqrt {21}

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