Question

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

Explanation:

Step1: Recall the sine function definition

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 40^{\circ}\), the opposite side to \(\theta\) is \(AC\), and the hypotenuse is \(10\).

Step2: Apply the sine formula

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

Step3: Solve for \(AC\)

Multiply both sides of the equation \(\sin(40^{\circ})=\frac{AC}{10}\) by \(10\). So, \(AC=(10)\sin(40^{\circ})\).

Answer:

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