4 multiple choice 1 point use the law of cosines. find b to the nearest tenth. 54.8 69.3 23.0 25.8

Question

Accepted Answer

# Explanation:
## Step1: Recall the Law of Cosines formula
The Law of Cosines formula is $b^{2}=a^{2}+c^{2}-2ac\cos B$. Here, $a = 42$, $c = 30$, and $B=32^{\circ}$.
## Step2: Substitute the values into the formula
$$
\begin{align*}
b^{2}&=42^{2}+30^{2}-2\times42\times30\times\cos(32^{\circ})\
b^{2}&=1764 + 900-2520\times0.8480\
b^{2}&=1764+900 - 2136.96\
b^{2}&=2664-2136.96\
b^{2}&=527.04\
b&=\sqrt{527.04}\
b&\approx23.0
\end{align*}
$$

# Answer:
23.0

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall the Law of Cosines formula

Step2: Substitute the values into the formula

Answer: