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Mechanical & Non-Mechanical Waves

If two sides ...

Question

If two sides $a, b$ and angle $A$ be such that two triangles are formed, then the sum of two values of the third side is

2 b s i n A

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2 b c o s A

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b / a c o s A

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(c + b) c o s A

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Solution

The correct option is C $2 b c o s A$
$c o s A = \frac{b^{2} + c^{2} - a^{2}}{2 b c}$
$c^{2} - 2 b c c o s A + b^{2} - a^{2} = 0$ ...(let $c_{1}, c_{2}$ be the two roots of this equation then using the quadratic equation propert) we can say that,
$c_{1} + c_{2} = 2 b c o s A$
$c_{1} c_{2} = b^{2} - a^{2}$

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