Question

3 multiple choice 1 point use the law of cosines. find b to the nearest tenth. 26.2 113.0 38.2 79.2

Explanation:

Step1: Apply the Law of Cosines formula

The Law of Cosines formula is \(b^{2}=a^{2}+c^{2}-2ac\cos B\). Here, \(a = 59\), \(c = 57\), and \(B=26^{\circ}\).
So, \(b^{2}=59^{2}+57^{2}-2\times59\times57\times\cos(26^{\circ})\).

Step2: Calculate each term

First, \(59^{2}=3481\), \(57^{2}=3249\).
\(\cos(26^{\circ})\approx0.8988\).
\(2\times59\times57 = 2\times3363=6726\).
\(6726\times0.8988\approx6046.5\).
Then \(b^{2}=3481 + 3249-6046.5\).
\(b^{2}=6730 - 6046.5=683.5\).

Step3: Find \(b\)

\(b=\sqrt{683.5}\approx 26.2\).

Answer:

\(26.2\)