Question

If two sides a, b and angle A be such that two triangles are formed, then the sum of the values of the third side is
1] 2b sin A
2] 2b cos A
3] b/a cos A
4] (c + b) cos A

Answer 1

4] (c + b) cos A
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Please mark the answer as brain list answer

Answer 2

The sum of the values of the third side is 2b cos A

Let the first root of quadratic equation be = c1

Let the second root of quadratic equation be = c2

From cosine formula, the equation will be -  

a² = b² + c² - 2 bc Cos A or

= c² - (2bcos A)c + b² - a² = 0, that is quadratic in point c

Therefore, as c1 and c2 are the roots of quadratic equation then, -  

The sum of two values of the third side will be -  

c1 + c2 = 2b cos A

Thus, the value of the third side is 2b cos A.