Question

which equation can be used to find the length of ac?
\\(\frac{10}{\sin(40^{\circ})}=ac\\)
\\((10)\sin(40^{\circ}) = ac\\)
\\(\frac{10}{\cos(40^{\circ})}=ac\\)
\\((10)\cos(40^{\circ}) = ac\\)

Explanation:

Step1: Recall trigonometric - ratio definition

In right - triangle ABC with right - angle at C, $\sin B=\frac{AC}{AB}$.

Step2: Identify given values

We know that $B = 40^{\circ}$ and $AB = 10$.

Step3: Substitute values into formula

$\sin(40^{\circ})=\frac{AC}{10}$.

Step4: Solve for AC

$AC=(10)\sin(40^{\circ})$.

Answer:

$(10)\sin(40^{\circ}) = AC$