find the exact value of sin a in simplest radical form.

Answer:

$\frac{\sqrt{52}}{14}=\frac{\sqrt{13}}{7}$

Explanation:

Step1: Recall sine - definition

In a right - triangle, $\sin A=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify opposite and hypotenuse

The side opposite to angle $A$ is $BC = \sqrt{52}$, and the hypotenuse $AB = 14$.

Step3: Simplify the fraction

$\sin A=\frac{\sqrt{52}}{14}=\frac{\sqrt{4\times13}}{14}=\frac{2\sqrt{13}}{14}=\frac{\sqrt{13}}{7}$.