Question

determining the sine ratio
what additional information would be necessary to determine sin(a) without using the pythagorean theorem? explain.
the length of ac is needed because it is the side adjacent to ∠a.
the length of ac is needed because it is the side opposite ∠a.
the length of bc is needed because it is the side opposite ∠a.
the length of bc is needed because it is the side adjacent to ∠a.

Explanation:

Recall the definition of the sine ratio in a right - triangle: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle A$ in right - triangle $ABC$ ($\angle C = 90^{\circ}$), the hypotenuse is $AB = 20$. The side opposite $\angle A$ is $BC$, and the side adjacent to $\angle A$ is $AC$. To find $\sin(A)=\frac{BC}{AB}$, since $AB$ is known ($AB = 20$), we need the length of the side opposite $\angle A$ (which is $BC$).

Answer:

C. The length of BC is needed because it is the side opposite $\angle A$.