Question

solve for x.
12
x°
22
32°
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: \( a = 22 \), opposite angle \( A = 32^\circ \); \( b = 12 \), opposite angle \( B = x^\circ \).

Step2: Apply Law of Sines

Using \(\frac{\sin A}{a}=\frac{\sin B}{b}\), substitute values: \(\frac{\sin 32^\circ}{22}=\frac{\sin x}{12}\).

Step3: Solve for \(\sin x\)

\(\sin x=\frac{12\times\sin 32^\circ}{22}\). Calculate \(\sin 32^\circ\approx0.5299\), so \(\sin x=\frac{12\times0.5299}{22}\approx\frac{6.3588}{22}\approx0.289\).

Step4: Find \(x\)

\(x=\arcsin(0.289)\approx16.82^\circ\).

Answer:

\(16.82\)