In ` A B C ,a , ca n dA` are given and `b_1,b_2` are two values of the third side `b` such that `b_2=2b_1dot` Then prove that `sinA=sqrt((9a^2-c^2)/(8c^2))`

Explanation

To prove that \( \sin A = \sqrt{\frac{9a^2 - c^2}{8c^2}} \) given the conditions in triangle \( ABC \) with sides \( a, b, c \) and two values of the third side \( b_1 \) and \( b_2 \) such that \( b_2 = 2b_1 \), we can follow these steps:

### Step 1: Use the Cosine Rule
From the cosine rule, we know that:
\[ \cos A = \frac{b^2 + c^2 - a^2}{2bc} \]

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