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: Solve for \( b \) from the equation

Given \( \sin(40^\circ) = \frac{b}{20} \), we can multiply both sides by \( 20 \) to isolate \( b \).
\( b = 20 \times \sin(40^\circ) \)

Step2: Calculate the value of \( \sin(40^\circ) \)

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

Step3: Compute \( b \)

Substitute the value of \( \sin(40^\circ) \) into the equation:
\( b = 20 \times 0.6428 = 12.856 \)

Step4: Round to the nearest tenth

Rounding \( 12.856 \) to the nearest tenth gives \( 12.9 \)

Answer:

B. 12.9 cm