Question

find fg.
write your answer as an integer or as a decimal rounded to the nearest tenth.
fg =

Explanation:

Step1: Identify trigonometric ratio

In right $\triangle EFG$, $\angle E=59^\circ$, hypotenuse $EG=7$, $FG$ is opposite $\angle E$. Use sine:
$\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute values and solve

Substitute $\theta=59^\circ$, hypotenuse$=7$:
$\sin(59^\circ)=\frac{FG}{7}$
Rearrange to solve for $FG$:
$FG=7\times\sin(59^\circ)$
Calculate $\sin(59^\circ)\approx0.8572$, so:
$FG\approx7\times0.8572$

Step3: Compute final value

$FG\approx6.0004$
Round to nearest tenth:
$FG\approx6.0$

Answer:

$6.0$