Right Triangle Trigonometry PBL Project | Clinometer Activity

Bring right triangle trigonometry to life with a hands-on Project Based Learning unit where students measure real trees, buildings, river widths, and ramps using a clinometer they build themselves. This 3–5 day Right Triangle Trigonometry PBL is designed for RTI Tier 2 intervention — rebuilding conceptual understanding of trigonometric ratios through authentic indirect measurement, not abstract memorization.

WHAT'S INSIDE (36 pages, print & digital ready):

✅ 4 Hands-On Measurement Stations — each with full procedure cards, data sheets, and exit tickets: • Station 1: Tree Height with a Clinometer (full build instructions from a protractor, straw, string, washer) • Station 2: Building Height via Shadows & Similar Triangles • Station 3: River Width using only a tape measure and a straw (set up in a hallway — no actual river needed!) • Station 4: Ramp Slope using a tangent ratio and a free inclinometer phone app, with an ADA compliance check

✅ Explicit vocabulary pre-teaching with visual anchors — opposite, adjacent, hypotenuse, angle of elevation, angle of depression

✅ Concept refresher on SOH CAH TOA with two fully worked examples

✅ I do / We do / You do procedure cards for every station (gradual release of responsibility)

✅ Detailed lucid solutions for every exit ticket and worked example — step-by-step, ready to hand to a student

✅ Tier 3 modified version — sin and cos only, calculator-supported frames, for students who need even more scaffolding

✅ Error-correction protocol — the 4-step Identify / Re-teach / Re-practice / Re-assess method, plus the 6 most common trig errors with targeted fixes

✅ Student reflection + real-world trig careers page (surveyor, civil engineer, architect, navigator, and more)

✅ Full answer key included

WHY THIS UNIT WORKS FOR RTI TIER 2: Students who struggle with abstract trigonometry instruction often fail at ratio selection — deciding whether to use sin, cos, or tan. This unit rebuilds the missing conceptual foundation through concrete → representational → abstract sequencing: students physically measure with a tape (concrete), label a diagram (representational), and only then compute with the tangent ratio (abstract). Every station is a real-world indirect-measurement problem drawn from the historical practice of surveying — the discipline that gave birth to trigonometry.

ALIGNED TO STANDARDS: • CCSS HSG-SRT.C.6 — Understand that by similarity, side ratios in right triangles are properties of the angles • CCSS HSG-SRT.C.8 — Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems • CCSS HSG-SRT.B.5 — Use congruence and similarity criteria for triangles to solve problems

GRADES: 9–11 | DURATION: 3–5 days | FORMAT: PDF (print & digital)

MATERIALS YOU'LL NEED: protractors, straws, string, washers, tape measures, calculators, and a free inclinometer phone app for Station 4. Most items are already in your classroom.