Question

solve for x.
14
83°
13
law of sines: \\(\frac{\sin a}{a} = \frac{\sin b}{b} = \frac{\sin c}{c}\\)
round your answer to the nearest hundredth.
\\(x = ?°\\)

Explanation:

Step1: Identify triangle parts

Let’s label the triangle: side \( a = 13 \) (opposite \( x^\circ \)), side \( b = 14 \) (opposite \( 83^\circ \)). Using Law of Sines: \( \frac{\sin x}{13} = \frac{\sin 83^\circ}{14} \)

Step2: Solve for \( \sin x \)

Multiply both sides by 13: \( \sin x = \frac{13 \cdot \sin 83^\circ}{14} \)
Calculate \( \sin 83^\circ \approx 0.9925 \), so \( \sin x \approx \frac{13 \cdot 0.9925}{14} \approx \frac{12.9025}{14} \approx 0.9216 \)

Step3: Find \( x \)

Take inverse sine: \( x = \arcsin(0.9216) \approx 67.28^\circ \) (rounded to nearest hundredth)

Answer:

\( 67.28 \)