Question

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

Explanation:

Step1: Recall sine - cosine definitions in right - triangle

In right - triangle $ABC$ with right angle at $C$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 40^{\circ}$, the hypotenuse $AB = 10$ in, and we want to find the length of $AC$ (opposite to angle $B$).

Step2: Apply the sine formula

Since $\sin B=\frac{AC}{AB}$, and $B = 40^{\circ}$, $AB = 10$ in. Substituting the values, we get $\sin(40^{\circ})=\frac{AC}{10}$.

Step3: Solve for $AC$

Cross - multiply the equation $\sin(40^{\circ})=\frac{AC}{10}$ to get $AC=(10)\sin(40^{\circ})$.

Answer:

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