Question

solve for x.
34
32
84°
x°
law of sines: \\(\frac{\sin a}{a} = \frac{\sin b}{b} = \frac{\sin c}{c}\\)
round your answer to the nearest hundredth.
\\(x = ?^\circ\\)

Explanation:

Step1: Apply Law of Sines

Let the side opposite \( x^\circ \) be 32, the side opposite \( 84^\circ \) be 34. By Law of Sines: \(\frac{\sin x}{32} = \frac{\sin 84^\circ}{34}\)

Step2: Solve for \(\sin x\)

Multiply both sides by 32: \(\sin x = \frac{32 \cdot \sin 84^\circ}{34}\)
Calculate \(\sin 84^\circ \approx 0.9945\), so \(\sin x \approx \frac{32 \cdot 0.9945}{34} \approx \frac{31.824}{34} \approx 0.936\)

Step3: Find \( x \)

Take inverse sine: \( x = \arcsin(0.936) \approx 69.51^\circ\)

Answer:

\( 69.51 \)