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

Question

Accepted Answer

# Explanation:
## Step1: Find the measure of angle $ E $
The sum of angles in a triangle is $ 180^{\circ} $.
$$
\begin{align*}
\angle E&=180^{\circ}-71^{\circ}-52^{\circ}\
& = 57^{\circ}
\end{align*}
$$
## Step2: Apply the Law of Sines
The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$.
For triangle $ EFG $, $\frac{f}{\sin F}=\frac{11}{\sin E}$.
Since $ F = 52^{\circ}$, $E = 57^{\circ}$, and the side opposite $ E $ is $ 11 $.
$$
\begin{align*}
f&=\frac{11\times\sin52^{\circ}}{\sin57^{\circ}}\
\sin52^{\circ}&\approx0.788, \sin57^{\circ}\approx0.839\
f&=\frac{11\times0.788}{0.839}\
&=\frac{8.668}{0.839}\
&\approx10.3
\end{align*}
$$

# Answer:
$10.3$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find the measure of angle \( E \)

Step2: Apply the Law of Sines

Answer: