Question

the equation \\(\sin(40^\circ) = \frac{b}{20}\\) can be used to determine the length of line segment \\(ac\\). what is the length of \\(\overline{ac}\\)? round to the nearest tenth. \\(\bigcirc\\) 11.8 cm \\(\bigcirc\\) 12.9 cm \\(\bigcirc\\) 14.9 cm \\(\bigcirc\\) 15.3 cm

Explanation:

Step1: Isolate $b$ in the equation

Multiply both sides by 20:
$$b = 20 \times \sin(40^\circ)$$

Step2: Calculate $\sin(40^\circ)$ and multiply

Use $\sin(40^\circ) \approx 0.6428$:
$$b \approx 20 \times 0.6428 = 12.856$$

Step3: Round to nearest tenth

Round 12.856 to one decimal place:
$$b \approx 12.9$$

Answer:

12.9 cm