Question

round your answer to the nearest hundredth.
law of sines:
\\( \frac { \sin a } { a } = \frac { \sin b } { b } = \frac { \sin c } { c } \\)
solve for x.
\\( x = \\)
\\( \square ^ { \circ } \\)

Explanation:

Step1: Apply the Law of Sines

According to the Law of Sines formula $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$, we have $\frac{\sin x}{27}=\frac{\sin28^{\circ}}{56}$.

Step2: Solve for $\sin x$

Cross - multiply to get $\sin x=\frac{27\times\sin28^{\circ}}{56}$.
Calculate $\sin28^{\circ}\approx0.4695$, then $\sin x=\frac{27\times0.4695}{56}\approx\frac{12.6765}{56}\approx0.2264$.

Step3: Find $x$

Take the inverse - sine of $0.2264$, so $x = \sin^{-1}(0.2264)\approx13.15^{\circ}$.

Answer:

$13.15$