Question

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

Explanation:

Step1: Recall the Law of Cosines formula

The Law of Cosines formula is \(b^{2}=a^{2}+c^{2}-2ac\cos B\). In \(\triangle ABC\), let \(a = 21\), \(c = 30\), and \(B=40^{\circ}\).

Step2: Substitute the values into the formula

Substitute \(a = 21\), \(c = 30\), and \(B = 40^{\circ}\) into \(b^{2}=a^{2}+c^{2}-2ac\cos B\).

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Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{375.7849017}\approx19.4\)

Answer:

19.4