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

Explanation:

The sine of an angle in a right triangle is defined as $\frac{\text{length of opposite side}}{\text{length of hypotenuse}}$. For $\angle A$, the hypotenuse is $AB = 20$, and the side opposite $\angle A$ is $BC$. To find $\sin(A)$ without the Pythagorean theorem, we need the length of the opposite side $BC$.

Answer:

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