Question

the equation $\sin(40^\circ) = \frac{b}{20}$ can be used to determine the length of line segment $\overline{ac}$. image of a right triangle with right angle at $c$, vertices $a$, $b$, $ac$ labeled $b$, $ab$ labeled $20$ cm, and $\angle b = 40^\circ$ 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: Solve for \( b \)

Given \( \sin(40^\circ) = \frac{b}{20} \), multiply both sides by 20:
\( b = 20 \times \sin(40^\circ) \)

Step2: Calculate \( \sin(40^\circ) \)

Using a calculator, \( \sin(40^\circ) \approx 0.6428 \)

Step3: Compute \( b \)

\( b = 20 \times 0.6428 \approx 12.856 \), round to nearest tenth: \( 12.9 \)

Answer:

B. 12.9 cm