Question

Suppose the area of the $△ABC$ is $10\sqrt{3}$. Length of the segments $AC$ and $AB$ be $5$ and $8$ respectively. Then the angle $A$ is (are)

• A. ${30}^o$ or ${150}^o$
• B. ${90}^o$
• C. ${60}^o$ or ${120}^o$
• D. ${45}^o$ or ${135}^o$

Answer 1

Answer: (C)

${60}^o$ or ${120}^o$

Let the length of sides $BC,CA$ and $AB$ be $a,b,c$ respectively
Given, $b=5$ and $c=8$
Area of $△ABC=\frac{1}{2}bc\sin A=10\sqrt{3}$

$\Rightarrow \frac{1}{2}\times 5\times 8\sin A=10\sqrt{3}$
$\Rightarrow \sin A=\frac{\sqrt{3}}{2}$
$\therefore \angle A={60}^{o}or{120}^o$