Question

right triangle abc is shown.
which equation can be used to solve for c?
a 3 m c
c 50° a
b
sin(50°) = 3/c
sin(50°) = c/3
cos(50°) = c/3
cos(50°) = 3/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 adjacent to angle \(B\) is \(AC = 3\) m and the hypotenuse is \(AB=c\).

Step2: Apply the cosine formula

Using the formula \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), with \(\theta = 50^{\circ}\), adjacent side \(=3\) and hypotenuse \(=c\).
We get \(\cos(50^{\circ})=\frac{3}{c}\)

Answer:

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