Question

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

Explanation:

Step1: Recall sine definition

In a right triangle, $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle E$, identify opposite and hypotenuse.
Opposite side to $\angle E$ is $FG = \sqrt{12}$, hypotenuse is $EG = 7$.

Step2: Simplify $\sqrt{12}$

$\sqrt{12} = \sqrt{4\times3} = 2\sqrt{3}$.

Step3: Compute $\sin E$

$\sin E = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{\sqrt{12}}{7} = \frac{2\sqrt{3}}{7}$.

Answer:

$\frac{2\sqrt{3}}{7}$