Question

solving for side lengths of right triangles. the equation sin(40°) = can be used to determine the length of line segment ac. what is the length of ac? round to the nearest tenth. 15.3 cm 12.9 cm 14.9 cm 11.8 cm

Explanation:

Step1: Recall sine - definition

In right - triangle \(ABC\) with right angle at \(C\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here \(\theta = 40^{\circ}\), the opposite side to \(\angle B\) is \(AC\) (let \(AC = b\)) and the hypotenuse \(AB = 20\mathrm{cm}\), so \(\sin(40^{\circ})=\frac{AC}{AB}=\frac{b}{20}\).

Step2: Solve for \(AC\)

We can rewrite the equation \(\sin(40^{\circ})=\frac{b}{20}\) as \(b = 20\times\sin(40^{\circ})\). Since \(\sin(40^{\circ})\approx0.6428\), then \(b=20\times0.6428 = 12.856\approx12.9\mathrm{cm}\).

Answer:

12.9 cm