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# When to use the law of sines V/S the law of cosines?

**Solution:**

For triangle ABC,

a = BC, b = AC, c = AB

The cosine rule states a^{2} = b^{2} + c^{2} - 2bc cos A, b^{2} = c^{2} + a^{2} - 2ac cos B, c^{2} = a^{2} + b^{2} - 2ab cos C, where a, b, c are the lengths of the sides opposite to angles A, B, and C, respectively, that is, BC, AC, AB

For triangle ABC,

The sine rule states a/sin A = b/sin B = c/sin C, where a, b, c are the lengths of the sides opposite to angles A, B, and C, respectively, that is, BC, AC, AB

The difference between the usage of the sine and cosine rule lies with the variables known to us at that moment. If all three sides are known to us then we can use the cosine rule to find all the angles of the triangle.

If 2 sides and one angle between them are known, then also we can use the cosine rule to find the remaining side and other angles between them.

If 2 angles and one side is known, we can easily find the third angle, and then use the sine rule to find all the remaining sides.

Thus, depending upon the variables given in the question, we can make use of either the sine or the cosine rule to find the remaining variables.

## When to use the law of sines V/S the law of cosines?

**Summary:**

Depending upon the variables given in the question, we can make use of either the sine or the cosine rule to find the remaining variables.

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