Question

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. (with a right triangle image labeled a, b, c with right angle at c and hypotenuse ab labeled 20)

Explanation:

To determine \(\sin(A)\) in a right - triangle, we use the definition \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). In \(\triangle ABC\) with \(\angle C = 90^{\circ}\), for \(\angle A\), the hypotenuse is \(AB = 20\). The side opposite \(\angle A\) is \(BC\), and the side adjacent is \(AC\). So, to find \(\sin(A)=\frac{BC}{AB}\), we need the length of \(BC\) (the side opposite \(\angle A\)) since we already know the hypotenuse.

Answer:

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