Question

in the figure below, what is ac?
15.98
cannot be determined
4
1.02

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines states that for a triangle with sides \(a\), \(b\), \(c\) and angle \(C\) opposite side \(c\), \(c^{2}=a^{2}+b^{2}-2ab\cos C\). In \(\triangle ABC\), let \(AB = c = 4.24\), \(BC=a = 3.23\), \(AC = b\), and \(\angle B=63^{\circ}\). Then \(b^{2}=a^{2}+c^{2}-2ac\cos B\).
Substitute \(a = 3.23\), \(c = 4.24\), and \(\cos B=\cos63^{\circ}\approx0.454\) into the formula:

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Step2: Solve for \(b\) (i.e., \(AC\))

Take the square - root of \(b^{2}=15.93\), \(b=\sqrt{15.93}\approx 4\)

Answer:

4