Question

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

Explanation:

Step1: Recall sine - cosine definitions

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

Step2: Apply the sine formula

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

Answer:

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