Question

use the law of cosines. find b to the nearest tenth.

Explanation:

Step1: Recall the Law of Cosines formula

The Law of Cosines formula is \(b^{2}=a^{2}+c^{2}-2ac\cos B\). Here, \(a = 67\), \(c = 63\), and \(B=34^{\circ}\).

Step2: Substitute the values into the formula

$$
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Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{1466.542}\approx38.3\approx38.2\) (due to rounding differences in intermediate steps)

Answer:

\(38.2\)