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

Explanation:

Step1: Identify the trig - ratio

In right - triangle $EFG$ with right - angle at $E$, we know the side $EF = 6.7$ and the angle $\angle G=53^{\circ}$. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\tan G=\frac{EF}{EG}$.

Step2: Rearrange the formula

We can rewrite the formula $\tan G=\frac{EF}{EG}$ as $EG=\frac{EF}{\tan G}$.

Step3: Substitute the values

We know that $EF = 6.7$ and $G = 53^{\circ}$, and $\tan53^{\circ}\approx1.3270$. So, $EG=\frac{6.7}{1.3270}$.

Step4: Calculate the value

$EG=\frac{6.7}{1.3270}\approx5.05$. Rounding to the nearest tenth, $EG\approx5.1$.

Answer:

$5.1$