Right Triangle Trigonometry Word Problem | AI Error Analysis 02

Is the AI right? Prove it. This Right Triangle Trigonometry word problem activity challenges high school geometry students to use the angle of elevation and trigonometric ratios (SOH CAH TOA) to find a missing height.

Instead of solving a standard worksheet, students are handed a printout from an AI assistant that just attempted to solve a real-world drone flight problem. The AI shows its work, but it made a critical mathematical error. Students must step into the role of a human auditor to find the mistake, explain the misconception, and fix the math before the film crew needlessly aborts a perfectly safe flight.

THE SCENARIO (The Error) A film crew needs to hover a drone safely above the Eiffel Tower's spire. They measure the horizontal distance along the ground and the angle of elevation. The AI calculates the target altitude, but it uses cosine instead of tangent. By calculating the diagonal line of sight (the hypotenuse) rather than the vertical altitude (the opposite leg), the AI falsely concludes the drone is too low and will crash. Students must reject the report, explain the cosine error, and provide the true, safe altitude.

WHAT STUDENTS DO (Steps & Outline)

1. Read the scenario and sketch the right triangle before seeing any numbers.

2. State the objective in one sentence.

3. Check their sketch against a verified diagram.

4. Audit the AI's output line by line.

5. File an Auditor's Report: reject the calculation, name the exact trigonometric error, and provide the correct altitude.

WHAT'S INCLUDED

• 2-Page Student Activity: Scenario, sketch box, verified diagram, the AI printout, and the official Auditor's Report.

• Full Teacher Answer Key: Completed report, corrected math, common student errors, and a holistic scoring guide (0-4 scale).

• "Make it Make Sense" Sidebar: A real-world analogy explaining the difference between measuring a diagonal path versus true vertical height.

PRODUCT DETAILS

• Grades: 9th, 10th, 11th, 12th (Geometry, Algebra 2, Precalculus)

• Format: Print-and-go PDF (Black & white, copier-friendly) & Digital Easel Activity

• Number of Pages: 4 pages total (2 student, 2 teacher)

• Best Used As: Bell-Ringer / Warm-Up, Check for Understanding (CFU), Exit Ticket, or a quick Sub Plan.

STANDARDS ALIGNMENT

• CCSS.MATH.CONTENT.HSG.SRT.C.8 — Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

• MP1 — Make sense of problems and persevere in solving them.

• MP3 — Construct viable arguments and critique the reasoning of others.