Question

solve for x.
27, x°, 44, 28°
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 \( 44 \), the side opposite \( 28^\circ \) be \( 27 \). By Law of Sines: \(\frac{\sin x}{44}=\frac{\sin 28^\circ}{27}\)

Step2: Solve for \(\sin x\)

Multiply both sides by \( 44 \): \(\sin x=\frac{44\sin 28^\circ}{27}\)
Calculate \(\sin 28^\circ\approx0.4695\), then \(\frac{44\times0.4695}{27}\approx\frac{20.658}{27}\approx0.7651\)

Step3: Find \( x \)

Take inverse sine: \( x=\arcsin(0.7651)\approx49.93^\circ\)

Answer:

\( 49.93 \)