Question

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

Explanation:

Step1: Recall sine definition

In a right triangle, $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle A$, opposite side is $BC = 2$, hypotenuse is $AB=\sqrt{5}$.

Step2: Apply sine formula

$\sin A = \frac{BC}{AB} = \frac{2}{\sqrt{5}}$. Rationalize the denominator: $\frac{2\sqrt{5}}{5}$.

Answer:

$\frac{2\sqrt{5}}{5}$