The triangle in the image asks to label its sides based on their relationship to the angle $\theta$: opposite, adjacent, and hypotenuse.

Here’s the breakdown:

1. Hypotenuse (DF):

   • The longest side of the right triangle, opposite the right angle ($\angle E$).

2. Opposite (DE):

   • The side directly opposite the angle $\theta$.

3. Adjacent (EF):

   • The side next to $\theta$, but not the hypotenuse.

Final Labels:

• $DE$: Opposite
• $EF$: Adjacent
• $DF$: Hypotenuse

Would you like further clarification or examples? 😊

Follow-Up Questions:

1. What are the trigonometric ratios (sine, cosine, tangent) based on these sides?
2. How do you identify the opposite and adjacent sides when the angle changes?
3. Why is the hypotenuse always the longest side in a right triangle?
4. Can the labels change if the reference angle shifts?
5. How do these sides relate to the Pythagorean Theorem?

Tip:

To remember trigonometric relationships, use the mnemonic SOH-CAH-TOA:

• Sine = Opposite / Hypotenuse
• Cosine = Adjacent / Hypotenuse
• Tangent = Opposite / Adjacent