Question

solve for x.
8
9
x°
55°
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 $\frac{\sin x}{9} = \frac{\sin 55^\circ}{8}$.

Step2: Solve for $\sin x$

Multiply both sides by 9: $\sin x = \frac{9 \cdot \sin 55^\circ}{8}$. Calculate $\sin 55^\circ \approx 0.8192$, so $\sin x \approx \frac{9 \cdot 0.8192}{8} \approx 0.9216$.

Step3: Find $x$

Take the inverse sine: $x \approx \arcsin(0.9216) \approx 67.22^\circ$.

Answer:

$67.22$