Question

find the length of \\(\overline{ac}\\) to the nearest tenth.\
\
\\(\bigcirc\\) 7.0\
\\(\bigcirc\\) 12.5\
\\(\bigcirc\\) 16.6\
\\(\bigcirc\\) 6.0

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(C) = \frac{AB}{AC}$

Step2: Rearrange to solve for $AC$

$AC = \frac{AB}{\sin(C)}$

Step3: Substitute given values

$AC = \frac{10}{\sin(53^\circ)}$

Step4: Calculate and round

$\sin(53^\circ) \approx 0.7986$, so $AC \approx \frac{10}{0.7986} \approx 12.5$

Answer:

12.5