find the measure of angle c.
round to the nearest tenth.

Question

Accepted Answer

# Explanation:
## Step1: Apply the Law of Cosines
The Law of Cosines formula is $a^{2}=b^{2}+c^{2}-2bc\cos A$. Here, $b = 3$, $c = 7$, and $A=60^{\circ}$. So, $a^{2}=3^{2}+7^{2}-2\times3\times7\times\cos60^{\circ}$.
$$
\begin{align*}
a^{2}&=9 + 49-42\times\frac{1}{2}\
a^{2}&=9+49 - 21\
a^{2}&=37\
a&=\sqrt{37}\approx6.1
\end{align*}
$$
## Step2: Apply the Law of Sines
The Law of Sines formula is $\frac{\sin B}{b}=\frac{\sin C}{c}=\frac{\sin A}{a}$. We know $b = 3$, $a\approx6.1$, and $A = 60^{\circ}$. Using $\frac{\sin C}{3}=\frac{\sin60^{\circ}}{6.1}$.
$$
\begin{align*}
\sin C&=\frac{3\times\sin60^{\circ}}{6.1}\
\sin C&=\frac{3\times\frac{\sqrt{3}}{2}}{6.1}\
\sin C&=\frac{3\times0.866}{6.1}\
\sin C&=\frac{2.598}{6.1}\approx0.426
\end{align*}
$$
$C=\sin^{-1}(0.426)\approx25.2^{\circ}$

# Answer:
$C\approx25.2^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Apply the Law of Cosines

Step2: Apply the Law of Sines

Answer: