Question

find the measure of angle c.
round to the nearest tenth.

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). But here, we can use the Law of Sines \(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\). First, let's label the sides: \(AB = 3\), \(AC=7\), \(\angle B = 60^{\circ}\).

Step2: Use the Law of Sines for \(\angle C\)

By the Law of Sines \(\frac{\sin C}{3}=\frac{\sin60^{\circ}}{7}\). Since \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\approx0.866\), then \(\sin C=\frac{3\times\sin60^{\circ}}{7}=\frac{3\times0.866}{7}\approx0.371\).

Step3: Find the angle \(C\)

\(C=\sin^{- 1}(0.371)\approx21.8^{\circ}\)

Answer:

\(21.8^{\circ}\)