Question

which equations could be used to solve for the unknown lengths of △abc? check all that apply.
□ sin(45°)=bc/9
□ sin(45°)=9/bc
□ 9 tan(45°)=ac
□ (ac)sin(45°)=bc
□ cos(45°)=bc/9

Explanation:

Step1: Recall sine - cosine - tangent definitions

In right - triangle ABC with right - angle at C and angle A = 45°, $\sin A=\frac{BC}{AB}$, $\cos A=\frac{AC}{AB}$, $\tan A=\frac{BC}{AC}$, and $AB = 9$.

Step2: Substitute values

$\sin(45^{\circ})=\frac{BC}{9}$, $(AC)\sin(45^{\circ})=BC$, $9\tan(45^{\circ})=AC$.

Answer:

$(AC)\sin(45^{\circ})=BC$, $9\tan(45^{\circ})=AC$, $\sin(45^{\circ})=\frac{BC}{9}$