Question

right triangle abc is shown. which equation can be used to solve for c? options: sin(50°) = 3/c, sin(50°) = c/3, cos(50°) = c/3, cos(50°) = 3/c (with triangle diagram: right triangle at c, ac=3 m, angle at b is 50°, hypotenuse c)

Explanation:

Step1: Recall trigonometric ratio definitions

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

Step2: Apply the cosine formula

\(\cos(50^{\circ})=\frac{\text{adjacent}}{\text{hypotenuse}}\). The adjacent side to angle \(B\) is \(BC\), and we are not using it for the correct formula related to the given side \(AC = 3\).
\(\sin(50^{\circ})=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the opposite side to angle \(B\) is \(AC = 3\) and the hypotenuse is \(AB = c\). So, \(\sin(50^{\circ})=\frac{3}{c}\)

Answer:

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