Question

the figure below shows a triangular piece of cloth: what is the length of the portion bc of the cloth? 8 cos 35° $\frac{sin35^{circ}}{8}$ $\frac{cos35^{circ}}{8}$ 8 sin 35°

Explanation:

Step1: Recall sine - definition

In right - triangle ABC with right - angle at B, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 35^{\circ}$, the hypotenuse $AC = 8$ inches and the side opposite to angle A is BC.

Step2: Apply the sine formula

We know that $\sin A=\frac{BC}{AC}$. Given $A = 35^{\circ}$ and $AC = 8$ inches. Substituting the values into the formula $\sin35^{\circ}=\frac{BC}{8}$.

Step3: Solve for BC

Cross - multiply the equation $\sin35^{\circ}=\frac{BC}{8}$ to get $BC = 8\sin35^{\circ}$.

Answer:

D. $8\sin35^{\circ}$