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:

To determine \(\sin(A)\) in a right - triangle, the formula is \(\sin(A)=\frac{\text{length of side opposite } \angle A}{\text{length of hypotenuse}}\). In \(\triangle ABC\) with right angle at \(C\), the hypotenuse is \(AB = 20\). The side opposite \(\angle A\) is \(BC\). So we need the length of \(BC\) (the side opposite \(\angle A\)) to calculate \(\sin(A)=\frac{BC}{AB}\) without using the Pythagorean theorem.

Answer:

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