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

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:

$6.0$