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.

Explanation:

Step1: Recall sine - function definition

The sine of an angle in a right - triangle is defined as $\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}$. In right - triangle $ABC$ with right - angle at $C$, for $\angle A$, the hypotenuse is $AB = 20$, and the opposite side to $\angle A$ is $BC$.

Step2: Determine needed side

To find $\sin(A)$ without using the Pythagorean theorem, we need the length of the side opposite to $\angle A$, which is $BC$.

Answer:

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