Two students describe the sides of right triangle ABC in relation to ∠B. 

Triangle A B C is shown. Angle A C B is a right angle. 	
Tomas
AB is the hypotenuse.

AC is the opposite side.

BC is the adjacent side.

Iliana
AB is the hypotenuse.

BC is the opposite side.

AC is the adjacent side.

Who is correct? Explain.

Tomas is correct; AC is opposite ∠B and BC is adjacent to ∠B.
Iliana is correct; BC is opposite ∠B and AC is adjacent to ∠B.
Both are correct because both AC and BC are opposite ∠B.
Neither is correct because neither AC nor BC is opposite ∠B.

Iliana is correct. 

In a right triangle, the side opposite a given angle is the one that does not touch that angle, and the side adjacent to a given angle is the one that touches it but is not the hypotenuse.

- **AB** is the **hypotenuse**, since it is the longest side and opposite the right angle ∠ACB.
- **BC** is **opposite ∠B** because it is the side that does not touch ∠B.
- **AC** is **adjacent to ∠B** because it touches ∠B but is not the hypotenuse.

Tomas has reversed the descriptions of the adjacent and opposite sides in relation to ∠B, while Iliana has described them correctly.

Would you like more details on how to identify the sides of a triangle based on angles?

Here are some related questions to deepen your understanding:

1. How do you find the hypotenuse in any right triangle?
2. What is the difference between opposite and adjacent sides in trigonometry?
3. How can you use trigonometric ratios to solve for sides in a right triangle?
4. How do the Pythagorean theorem and trigonometric ratios relate to the sides of a right triangle?
5. What are some common mistakes students make when identifying opposite and adjacent sides?

**Tip:** When identifying the opposite and adjacent sides, always start by locating the given angle, then remember that the hypotenuse is always the longest side opposite the right angle.

Two students describe the sides of right triangle ABC in relation to ∠B. Triangle A B C is shown. Angle A C B is a right angle. Tomas: AB is the hypotenuse. AC is the opposite side. BC is the adjacent side. Iliana: AB is the hypotenuse. BC is the opposite side. AC is the adjacent side. Who is correct? Explain.

This problem helps students identify the hypotenuse, adjacent, and opposite sides of a right triangle based on a given angle (∠B). The solution clarifies common student mistakes and strengthens understanding of trigonometric concepts. Suitable for Grades 8-10 students.

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