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

\[\cos A = \frac{b^2 + c^2 - a^2}{2bc}\]

\[ \Rightarrow \cos30° = \frac{\left( \sqrt{3} \right)^2 + \left( 1 \right)^2 - a^2}{2 \times \sqrt{3} \times 1}\]

\[ \Rightarrow \frac{\sqrt{3}}{2} = \frac{4 - a^2}{2\sqrt{3}}\]

\[ \Rightarrow 3 = 4 - a^2 \]

\[ \Rightarrow a^2 = 4 - 3 = 1\]

\[ \Rightarrow a = 1\]

Concept: Sine and Cosine Formulae and Their Applications

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