Question

solve for x.
27
x°
44
28°
x = ?°
law of sines: \\(\frac{\sin a}{a} = \frac{\sin b}{b} = \frac{\sin c}{c}\\)

Explanation:

Step1: Identify sides and angles

Let the triangle have sides: \( a = 44 \) (opposite \( x^\circ \)), \( b = 27 \) (opposite \( 28^\circ \)). Using Law of Sines: \( \frac{\sin x}{44} = \frac{\sin 28^\circ}{27} \)

Step2: Solve for \( \sin x \)

\( \sin x = \frac{44 \times \sin 28^\circ}{27} \)
Calculate \( \sin 28^\circ \approx 0.4695 \)
\( \sin x \approx \frac{44 \times 0.4695}{27} \approx \frac{20.658}{27} \approx 0.7651 \)

Step3: Find \( x \)

\( x \approx \arcsin(0.7651) \approx 50^\circ \) (checking for triangle validity, since \( 44 > 27 \), \( x > 28^\circ \), and \( 180 - 28 - 50 = 102^\circ \), which is valid)

Answer:

\( 50 \)