Math, asked by rgpaudel468, 1 month ago

verify the sine law by taking particular triangle in four quadrants

Answers

Answered by manasijena8679
10

Suppose a, b and c represent the sides of a triangle ABC in magnitude and direction. Then we have a+b+c=0 by triangular law of forces. a x a + a x b + a x c = 0. So a x b = c x a.

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Answered by XXITZFLIRTYQUEENXX
5

Suppose a, b and c represent the sides of a triangle ABC in magnitude and direction.

Then we have a+b+c=0 by triangular law of forces.

Taking cross product with vector a we have

a x a + a x b + a x c = 0. So a x b = c x a. Similarly, b x c = c x a.Hence a x b = b x c = c x a

Therefore, |a x b| = |b x c| = |c x a|

So, ab sin C = bc sin A = ca sin B

Divide throughout by abc and take reciprocals

We get a/sin A = b/ sin B = c/ sin C which is the sine rule in a triangle.

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