Question

triangle abc is shown. which equation can be used to solve for c? a 3 m c a c 50° b

Explanation:

Step1: Recall trigonometric - ratio definitions

In right - triangle \(ABC\) with right - angle at \(C\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). The angle \(\theta = 50^{\circ}\), the side adjacent to the \(50^{\circ}\) angle is \(3\) (side \(BC\)), and the hypotenuse is \(c\) (side \(AB\)).

Step2: Identify the correct trigonometric ratio

We know that \(\sin(50^{\circ})=\frac{\text{opposite}}{\text{hypotenuse}}\). The side opposite the \(50^{\circ}\) angle is \(a\) and the hypotenuse is \(c\). Also, \(\cos(50^{\circ})=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{3}{c}\).

Answer:

\(\cos(50^{\circ})=\frac{3}{c}\)