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Question
Answer the following questions in one word or one sentence or as per exact requirement of the question.In a ∆ABC, if b =\[\sqrt{3}\] and \[\angle A = 30°\] find a.
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Solution
In ∆ABC, b = \[\sqrt{3}\] c = 1 and [\angleA = 30°\]
Using cosine formula, we have
\[\cos A = \frac{b^2 + c^2 - a^2}{2bc}\]
\[ \Rightarrow \cos30° = \frac{\left( \sqrt{3} \right)^2 + \left( 1 \right)^2 - a^2}{2 \times \sqrt{3} \times 1}\]
\[ \Rightarrow \frac{\sqrt{3}}{2} = \frac{4 - a^2}{2\sqrt{3}}\]
\[ \Rightarrow 3 = 4 - a^2 \]
\[ \Rightarrow a^2 = 4 - 3 = 1\]
\[ \Rightarrow a = 1\]
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