Question

solve for x.
8
x°
9
55°
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: side opposite \( x^\circ \) is 9, side opposite \( 55^\circ \) is 8. Let \( A = x^\circ \), \( a = 9 \), \( B = 55^\circ \), \( b = 8 \).
Using Law of Sines: \( \frac{\sin A}{a}=\frac{\sin B}{b} \)

Step2: Substitute values

Substitute \( a = 9 \), \( b = 8 \), \( B = 55^\circ \) into the formula:
\( \frac{\sin x}{9}=\frac{\sin 55^\circ}{8} \)
Multiply both sides by 9: \( \sin x=\frac{9\sin 55^\circ}{8} \)
Calculate \( \sin 55^\circ\approx0.8192 \), so \( \sin x=\frac{9\times0.8192}{8}=\frac{7.3728}{8}=0.9216 \)

Step3: Find \( x \)

Take inverse sine: \( x=\arcsin(0.9216) \)
Calculate \( x\approx67.22^\circ \) (rounded to nearest hundredth)

Answer:

\( 67.22 \)