Question

solve for x.
20
17
x°
64°
x = ?°
law of sines: \frac{\sin a}{a} = \frac{\sin b}{b} = \frac{\sin c}{c}
round your answer to the nearest hundredth.

Explanation:

Step1: Apply Law of Sines

Using the Law of Sines formula $\frac{\sin x}{17} = \frac{\sin 64^\circ}{20}$.

Step2: Solve for $\sin x$

Multiply both sides by 17: $\sin x = \frac{17 \times \sin 64^\circ}{20}$.
Calculate $\sin 64^\circ \approx 0.8988$, so $\sin x \approx \frac{17 \times 0.8988}{20} \approx \frac{15.2796}{20} \approx 0.76398$.

Step3: Find $x$

Take the inverse sine: $x = \arcsin(0.76398) \approx 49.83^\circ$.

Answer:

$49.83$