5 multiple choice 1 point use the law of cosines. find b to the nearest tenth. 37.7 19.9 19.4 48.0

Question

Accepted Answer

# Explanation:
## Step1: Recall the Law of Cosines formula
The Law of Cosines formula is $b^{2}=a^{2}+c^{2}-2ac\cos B$. In this triangle, $a = 30$, $c = 21$, and $B=40^{\circ}$.
## Step2: Substitute the values into the formula
$$
\begin{align*}
b^{2}&=30^{2}+21^{2}-2\times30\times21\times\cos(40^{\circ})\
b^{2}&=900 + 441-1260\times\cos(40^{\circ})\
\end{align*}
$$
We know that $\cos(40^{\circ})\approx0.7660$.
$$
\begin{align*}
b^{2}&=900 + 441-1260\times0.7660\
b^{2}&=1341-965.16\
b^{2}&=375.84\
b&=\sqrt{375.84}\
b&\approx19.4
\end{align*}
$$

# Answer:
19.4

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Question

Explanation:

Step1: Recall the Law of Cosines formula

Step2: Substitute the values into the formula

Answer: