Question #dc21d

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Question #dc21d

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Answer 1 · 2017-04-22T10:56:38

The two factories are $2201$ $2201$ meter apart.

Explanation:

Assume the velocity of sound in air as $343$ $343$ metres per second. A is the position of man , B is the position of one factory and C is the position of other factory.

$A B (c) = 1.4 \cdot 343 = 480.2$ $AB(c) = 1.4*343 = 480.2$ metres ; $A C (b) = 6.9 \cdot 343 = 2366.7$ $AC (b)= 6.9 *343 =2366.7$ metres. Included angle between sides $b and c$ $b and c$ is $∠ A = {64.3}^{0}$ $/_A=64.3^0$

Applying cosine law for a triangle we get $B C (a) = \sqrt{b^{2} + c^{2} - 2 b c cos A} or a = \sqrt{{2366.7}^{2} + {480.2}^{2} - 2 \cdot 2366.7 \cdot 480.2 \cdot cos 64.3} = 2201$ $BC(a)=sqrt( b^2+c^2-2bc cosA) or a= sqrt(2366.7^2+480.2^2-2*2366.7*480.2*cos64.3)= 2201$ metres.

The two factories are $2201$ $2201$ meter apart. [Ans]

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Question #dc21d

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