Question

right triangle abc is shown. which equation can be used to solve for c? diagram: right triangle with right angle at c, segment ac = 3 m, segment ab = c, segment bc = a, angle at b is 50° options: \\( \sin(50^\circ) = \frac{3}{c} \\); \\( \sin(50^\circ) = \frac{c}{3} \\); \\( \cos(50^\circ) = \frac{c}{3} \\); \\( \cos(50^\circ) = \frac{3}{c} \\)

Explanation:

Step1: Recall SOHCAHTOA

In a right triangle, \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\).
For \(\angle B = 50^\circ\), side \(AC = 3\) m is opposite to \(\angle B\), and \(c\) is the hypotenuse.

Step2: Apply Sine Definition

Using \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\), with \(\theta = 50^\circ\), opposite \(= 3\), hypotenuse \(= c\), we get \(\sin(50^\circ)=\frac{3}{c}\).

Answer:

\(\sin(50^\circ)=\frac{3}{c}\) (the first option)