Question

Law of Sines, due by tonight

Answer 1

`21^(\circ)`

Explanation:

The Law of Sines is given by
`(\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c)` and works for every triangle.

Substituting given values, we have the following equation:

`(\sin 68^(\circ))/(18)=(\sin C)/(7), \\\\\sin C=(7\sin 68^(\circ))/(18),\\\\C=\sin^(-1)(0.36057149899),\\\\C\approx \boxed{21^(\circ)}`

*Note that because
`\sin \theta=\sin(180-\theta)`, when solving for an angle with the Law of Sines, there may be two answers. However, since the problem designates angle C as an acute angle, the other angle is negligible.