This game uses one fixed right triangle: AC = 9, BC = 12, AB = 15, with the right angle at C. For A, sine is 12/15 = 4/5; for B, sine is 9/15 = 3/5. The HTML activity checks side names and exact fractions in two angle rounds, then asks learners to explain why "sin A = 9/15" uses the wrong numerator.
Fix the geometry before choosing roles
Place C at (0,0), A at (9,0), and B at (0,12) in consistent drawing units. Join A to B and mark the right angle at C. The side lengths satisfy 9² + 12² = 81 + 144 = 225 = 15².
AB remains the hypotenuse because it lies opposite the right angle. The adjacent leg is the leg beside the chosen acute angle, excluding that hypotenuse. OpenStax's right-triangle trigonometry lesson explains ratios relative to the selected angle.
Use the side names before the fractions. A correct number can conceal a mistaken role, especially when a learner remembers one fraction from the previous round. The activity therefore asks for Opposite, Adjacent leg, and Hypotenuse as well as sine, cosine, and tangent.
Build the three ratios for A
Relative to A, BC is opposite with length twelve, AC is the adjacent leg with length nine, and AB is the hypotenuse with length fifteen. Sine A is BC/AB = 12/15 = 4/5.
Cosine A is AC/AB = 9/15 = 3/5. Tangent A is BC/AC = 12/9 = 4/3. Keep the original side-ratio trace beside the reduced fractions so learners can explain which lengths supplied the numerator and denominator.
The answer fields begin blank. The checker accepts equivalent positive fractions, such as 12/15 for 4/5, while the teacher reads the learner's explanation. It does not need a measured angle or a decimal estimate.
Switch to B without changing lengths
For B, AC becomes opposite and BC becomes the adjacent leg. AB is still the hypotenuse. Sine B is 9/15 = 3/5, cosine B is 12/15 = 4/5, and tangent B is 9/12 = 3/4.
Nothing moved: AC is still nine and BC is still twelve. The chosen reference angle changed the two leg roles. This also explains why sine A equals cosine B in this triangle; both ratios use BC/AB.
Switching rounds clears visible prior feedback and loads that round's blank or current attempt. A correct A response cannot silently become a correct B response. The diagram and text both identify the current angle so the reader can check the context before entering ratios.
Explain the distractor
Round three proposes "sin A = 9/15." Reject it because AC = 9 is adjacent to A. That ratio is cosine A. Sine A needs the opposite side BC = 12 over hypotenuse AB = 15.
Name the wrong side before correcting the fraction. This gives the explanation a geometric basis. Accepting or rejecting the statement alone supplies less information than explaining how its numerator was chosen.
Copy this prompt
Create one self-contained US-English HTML right-triangle reasoning game. Use an original proportional triangle ABC with C(0,0), A(9,0), B(0,12), right angle C, AC=9, BC=12, AB=15. Label sides and vertices clearly and provide complete text equivalents. Use minimum 16px text, visible focus, and a 360px responsive layout. No remote dependencies or persistence.
Provide three fixed round buttons. Round A asks for opposite, adjacent leg, hypotenuse, sin, cos, tan, and explanation. Key BC/AC/AB and 4/5,3/5,4/3. Round B uses AC/BC/AB and 3/5,4/5,3/4. Angle changes swap leg roles, never lengths or hypotenuse. Display the selected reference angle in diagram and text.
Use labeled blank text inputs for side names and fractions. A type=button Check accepts either endpoint order for each segment, such as BC/CB, while preserving opposite/adjacent/hypotenuse field roles. Validate positive integer fractions, equivalent exact ratios, missing or invalid answers, and explain the reference-angle change. Reject zero denominators. Reasons remain teacher-reviewed.
Round three asks Accept/Reject for sin A = 9/15. Correct rejection explains AC is adjacent for A, so 9/15 is cos A; sine uses BC/AB = 12/15 = 4/5. Provide a separate explanation field.
Keep responses attached to round IDs, clear stale feedback when editing or switching, and include Reset that clears all attempts. Reveal a separate teacher derivation without replacing learner fields. Preserve three unique rounds; no measured-angle estimate, arbitrary triangle solver, inverse functions, student collection, scores, or mastery claim. Use explicit selectors and click handlers, with a plain-text answer trace available without the diagram. Return complete HTML.
Prepare the A/B comparison and distractor together, then preview the HTML in NOS if a readable triangle-and-ratio page helps your lesson preparation. Keep the lesson handout and actual learner explanations, and finish by asking which side stays the hypotenuse when the reference angle changes.