Question

the equation \\(\sin(40^\circ) = \frac{b}{20}\\) can be used to determine the length of line segment ac.

triangle image with right angle at c, side ab = 20 cm, angle at b is 40°

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 \(20\) to isolate \(b\): \(b = 20\times\sin(40^{\circ})\).

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

Using a calculator, \(\sin(40^{\circ})\approx0.6428\).

Step3: Calculate the value of \(b\)

Substitute \(\sin(40^{\circ})\approx0.6428\) into \(b = 20\times\sin(40^{\circ})\). Then \(b=20\times0.6428 = 12.856\approx12.9\) (rounded to the nearest tenth).

Answer:

12.9 cm