Question

find eg.
write your answer as an integer or as a decimal rounded to the nearest tenth.
eg =
submit
work it out

Explanation:

Step1: Identify trigonometric ratio

In right $\triangle EFG$, $\angle E=58^\circ$, side opposite $\angle E$ is $GF=\sqrt{67}$, and $EG$ is the hypotenuse. Use sine:
$\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(58^\circ)=\frac{\sqrt{67}}{EG}$

Step3: Solve for $EG$

Rearrange to isolate $EG$:
$EG=\frac{\sqrt{67}}{\sin(58^\circ)}$
Calculate $\sqrt{67}\approx8.185$, $\sin(58^\circ)\approx0.8480$
$EG\approx\frac{8.185}{0.8480}\approx9.65$

Step4: Round to nearest tenth

Round 9.65 to 9.7

Answer:

9.7