Question

using the law of sines, which ratio can help you correctly find the value of angle ( a )?
(1 point)
( \bigcirc ) ( \frac{sin a}{10} = \frac{sin 85^circ}{15} )
( \bigcirc ) ( \frac{sin a}{15} = \frac{sin 85^circ}{10} )
( \bigcirc ) ( \frac{sin a}{15} = \frac{sin 85^circ}{40} )
( \bigcirc ) ( \frac{sin a}{15} = \frac{sin 40^circ}{10} )

Explanation:

Step1: Recall Law of Sines

The Law of Sines states:
$$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$$
where side $a$ is opposite $\angle A$, side $b$ opposite $\angle B$, side $c$ opposite $\angle C$.

Step2: Match sides to angles

For $\angle A$, opposite side is $a = 10$ in.
For $\angle B = 85^\circ$, opposite side is $b = 15$ in.
Substitute into Law of Sines:
$$\frac{\sin A}{10} = \frac{\sin 85^\circ}{15}$$

Answer:

$\frac{\sin A}{10} = \frac{\sin 85^\circ}{15}$ (the first option)