# Answer the Following Questions in One Word Or One Sentence Or as per Exact Requirement of the Question.In a ∆Abc, If B = √ 3 and ∠ a = 30 ° Find A. - Mathematics

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

#### 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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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 10 Sine and cosine formulae and their applications
Q 2 | Page 26