If you are given two $\mathrm{angles}$ in a $\mathrm{right}\mathrm{triangle}$, what additional information do you need to determine all the $\mathrm{side}\mathrm{lengths}$ of the $\mathrm{triangle}$?

• A. No additional information is needed; the $\mathrm{side}\mathrm{lengths}$ can be found from the $\mathrm{angles}$ alone.
• B. You need the $\mathrm{area}$ of the $\mathrm{triangle}$.
• C. You need the $\mathrm{length}$ of at least one $\mathrm{side}$.
• D. You need the $\mathrm{length}$ of the $\mathrm{hypotenuse}$ and one $\mathrm{leg}$.

Answer: (C)

Verified step by step guidance

1. Recall that in a right triangle, the sum of the angles is always 180 degrees, and one angle is 90 degrees by definition.
2. If you are given two angles, you actually know all three angles of the triangle, since the third angle is 90 degrees minus the sum of the other two.
3. Knowing all the angles alone only gives you the shape of the triangle, but not the size; the triangle could be similar to many others with different side lengths.
4. To find the actual side lengths, you need at least one side length as a reference or scale.
5. Once you have one side length and all the angles, you can use trigonometric ratios such as sine, cosine, and tangent to find the other side lengths.