Question

solve for x.
18
9
x = ?°
x°
83°
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

Let the side opposite \( x^\circ \) be 9, the side opposite \( 83^\circ \) be 18. By Law of Sines: \(\frac{\sin x}{9} = \frac{\sin 83^\circ}{18}\)

Step2: Solve for \(\sin x\)

Multiply both sides by 9: \(\sin x = \frac{9 \cdot \sin 83^\circ}{18}\) Simplify: \(\sin x = \frac{\sin 83^\circ}{2}\) Calculate \(\sin 83^\circ \approx 0.9925\), so \(\sin x \approx \frac{0.9925}{2} \approx 0.49625\)

Step3: Find \( x \)

Take inverse sine: \( x \approx \arcsin(0.49625) \approx 29.77^\circ \)

Answer:

\( 29.77 \)