Question

solve for x.
14
x°
13
83°
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: Identify sides and angles

Let the triangle have sides: \( a = 13 \), \( b = 14 \), angle \( B = 83^\circ \), angle \( A = x^\circ \).

Step2: Apply Law of Sines

Using \(\frac{\sin A}{a}=\frac{\sin B}{b}\), substitute values: \(\frac{\sin x}{13}=\frac{\sin 83^\circ}{14}\).

Step3: Solve for \(\sin x\)

\(\sin x=\frac{13\times\sin 83^\circ}{14}\). Calculate \(\sin 83^\circ\approx0.9925\), so \(\sin x=\frac{13\times0.9925}{14}\approx\frac{12.9025}{14}\approx0.9216\).

Step4: Find \(x\)

\(x=\arcsin(0.9216)\approx67.22^\circ\) (rounded to nearest hundredth).

Answer:

\( 67.22 \)