right triangle abc is shown. which equation can be used to solve for c? sin(50°) = 3/c sin(50°) = c/3…

right triangle abc is shown. which equation can be used to solve for c? sin(50°) = 3/c sin(50°) = c/3 cos(50°) = c/3 cos(50°) = 3/c

right triangle abc is shown. which equation can be used to solve for c? sin(50°) = 3/c sin(50°) = c/3 cos(50°) = c/3 cos(50°) = 3/c

Answer

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 right - angle at $C$, for angle $B = 50^{\circ}$, the side opposite to angle $B$ is $AC = 3$ and the hypotenuse is $AB=c$.

Step2: Apply the sine formula

By the definition of the sine function, $\sin B=\frac{AC}{AB}$. Substituting $B = 50^{\circ}$, $AC = 3$, and $AB = c$, we get $\sin(50^{\circ})=\frac{3}{c}$.

Answer:

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