Question

solve for x.
34
x°
32
84°
law of sines: \\(\frac{\sin a}{a} = \frac{\sin b}{b} = \frac{\sin c}{c}\\)
\\(x = ?^\circ\\)

Explanation:

Step1: Identify sides and angles

Let the triangle have sides: \( a = 32 \) (opposite \( x^\circ \)), \( b = 34 \) (opposite \( 84^\circ \)). Using Law of Sines: \( \frac{\sin x}{32} = \frac{\sin 84^\circ}{34} \)

Step2: Solve for \( \sin x \)

\( \sin x = \frac{32 \cdot \sin 84^\circ}{34} \)
Calculate \( \sin 84^\circ \approx 0.9945 \)
\( \sin x \approx \frac{32 \cdot 0.9945}{34} \approx \frac{31.824}{34} \approx 0.936 \)

Step3: Find \( x \)

\( x \approx \arcsin(0.936) \approx 69^\circ \) (checking triangle angle sum, other angle is \( 180 - 84 - 69 = 27^\circ \), valid)

Answer:

\( 69 \) (approximate, depending on calculator precision)