Question

right triangle abc is shown. which equation can be used to solve for c?
a
3 m
c
\\( \sin ( 50 ^ { \circ } ) = \frac { 3 } { c } \\)
\\( \sin ( 50 ^ { \circ } ) = \frac { c } { 3 } \\)
\\( \cos ( 50 ^ { \circ } ) = \frac { c } { 3 } \\)
\\( \cos ( 50 ^ { \circ } ) = \frac { 3 } { c } \\)
b

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Identify the sides with respect to the given angle

For angle \(B = 50^{\circ}\), the adjacent side is \(AC = 3\) and the hypotenuse is \(AB=c\).

Step3: Apply the cosine formula

Substituting into \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), we get \(\cos(50^{\circ})=\frac{3}{c}\).

Answer:

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