Question

right triangle abc is shown. which equation can be used to solve for c? a 3 m c a c 50° 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 $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. In right - triangle $ABC$ with respect to angle $B = 50^{\circ}$, the side opposite to angle $B$ is $AC = 3$ m and the hypotenuse is $AB=c$.

Step2: Apply the sine formula

Using the formula $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, when $\theta = 50^{\circ}$, we have $\sin(50^{\circ})=\frac{3}{c}$.

Answer:

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