Question

right triangle abc is shown. solving for side lengths of right triangles. which equation can be used to solve for c? options: \\(\sin(50^{\circ}) = \frac{3}{c}\\), \\(\cos(50^{\circ}) = \frac{3}{c}\\), \\(\sin(50^{\circ}) = \frac{c}{3}\\), \\(\cos(50^{\circ}) = \frac{c}{3}\\)

Explanation:

Step1: Identify sides relative to angle B

In right triangle \(ABC\), \(\angle C = 90^\circ\), \(\angle B = 50^\circ\), side \(AC = 3\) m (opposite \(\angle B\)), and hypotenuse \(AB = c\).

Step2: Recall sine definition

Sine of an angle in a right triangle is \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle B = 50^\circ\), opposite side is \(AC = 3\), hypotenuse is \(c\). So \(\sin(50^\circ)=\frac{3}{c}\).

Answer:

\(\boldsymbol{\sin(50^\circ)=\frac{3}{c}}\) (matching the first option among the choices, likely the one labeled with \(\sin(50^\circ)=\frac{3}{c}\))