Question

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

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

Answer 1

The correct option is D ${60}^{\circ }$ or ${120}^{\circ }$

Area of the triangle
$=\frac{1}{2}\times 8\times 5\sin \theta =10\sqrt{3}$
$\Rightarrow \sin \theta =\frac{\sqrt{3}}{2}\Rightarrow \theta ={60}^{\circ }\text{or}{120}^{\circ }$