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. $11.8$ cm $12.9$ cm $14.9$ cm $15.3$ cm

Explanation:

Step1: Solve the equation 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, \( \sin(40^{\circ})\approx0.6428 \)

Step3: Compute \( b \)

\( b = 20\times0.6428 = 12.856\approx12.9 \)

Answer:

12.9 cm