My son is in 9th grade geometry / intro
Ask
My son is in 9th grade geometry / intro trig and consistently makes the same error in word problems: he picks the wrong trig ratio (e.g., uses sine when he should use cosine, or uses tangent when he should use sine) because he labels "opposite" and "adjacent" incorrectly relative to the angle he's working from.
For example, in a problem like "a ramp is 12 feet long and makes a 30° angle with the ground — what is the height?" — he labels the ramp as the adjacent side instead of the hypotenuse, so he sets up the wrong ratio and gets the wrong answer.
The procedural mnemonic (SOHCAHTOA) he has memorized fine. The error is happening BEFOE the formula — when he's drawing or labeling the triangle.
Could you help me:
1. What's the most reliable way to teach a student to correctly identify the reference angle first, THEN label opposite/adjacent/hypotenuse relative to that specific angle (not the triangle in general)?
2. Is there a visual or physical setup strategy (drawing a consistent "POV" or "standing at the angle" mental trick) that helps students avoid swapping opposite and adjacent?
3. What kind of targeted practice problem would specifically drill the labeling step without letting the student jump to the formula?
I want to guide him through the labeling process himself — not give him the answer.
Answer
The fix isn't more SOHCAHTOA — he has that. The fix is **anchoring the labels to one chosen vertex, not to the picture.** SOHCAHTOA assumes you've already done that. He's skipping it.
**Cause in one sentence (you say this out loud before each problem):**
*"The sides are named from the angle the problem is asking about, not from the triangle in general."*
**Three questions for tonight, in this order:**
1. **"Put your finger on the angle the question is asking about. Now — without moving your finger, name the three sides from that spot."**
*You'll know it landed if* he names one as "opposite the angle I'm pointing at." If he names them by length or by what's in the picture ("the ramp," "the bottom"), the anchoring didn't happen.
2. **"Cover the right-angle corner with your thumb. What's the only side you can still see?"**
*You'll know it landed if* he points to the slant. The name comes after — if he calls it hypotenuse, the rule landed; if he calls it "the long one" or "the ramp," it didn't.
3. **"Look at the two sides your finger is touching. One of them is the hypotenuse. How do you know which?"**
*You'll know it landed if* his reason is "it's the one across from the 90°," not "it's the longest" or "it's the slanted one." If his reason is length or picture, the labeling is still anchored to the wrong thing.
**The pencil-trick that makes 1–3 automatic:**
Touch the vertex of your chosen angle with your pencil tip. The side your pencil does NOT touch = **opposite**. The side across from the 90° (the one still showing in question 2) = **hypotenuse**. Whatever's left = **adjacent**. That's the whole rule — "stand at the angle" is the same rule said in a more confusing way.
**Targeted drill — labeling only, no formula:**
A page with 5 right triangles, each in a different orientation (right-angle corner varies, reference angle at top / bottom / left / right). Mark one acute angle with a small arc. Three sides labeled with letters or lengths. He writes only:
- opposite to the marked angle = ___
- adjacent to the marked angle = ___
- hypotenuse = ___
Once he gets 5/5, the next page can ask for the ratio. Until then, no formula — it's the labeling step that's tripping him.
**What does NOT fix it:** more SOHCAHTOA drills, coloring sides by length, memorizing "the ramp is the hypotenuse." Those all skip the anchoring step he's missing.
If you want a 6-triangle printable for tonight, say the word and I'll make the sheet.