# Chapter 7 - Applications of Trigonometry and Vectors - Section 7.3 The Law of Cosines - 7.3 Exercises - Page 324: 75a

The two candidates for the value of angle $C$ are $87.8^{\circ}$ and $92.2^{\circ}$

#### Work Step by Step

We can use the law of sines to find candidates for angle $C$: $\frac{a}{sin~A} = \frac{c}{sin~C}$ $sin~C = \frac{c~sin~A}{a}$ $C = arcsin(\frac{c~sin~A}{a})$ $C = arcsin(\frac{15~sin~60^{\circ}}{13})$ $C = arcsin(0.99926)$ $C = 87.8^{\circ}$ Another possible value for angle $C$ is $180^{\circ}-87.8^{\circ}$ which is $92.2^{\circ}$ The two candidates for the value of angle $C$ are $87.8^{\circ}$ and $92.2^{\circ}$

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