Right Triangle Trigonometry PBL Project | Clinometer Activity
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Quick overview
## About the Resource
The **Right Triangle Trigonometry PBL Unit** is a hands-on **Grades 9–11 math intervention resource** that helps students connect **SOH-CAH-TOA, trigonometric ratios, indirect measurement, angle of elevation, and right-triangle problem solving** to authentic situations.
Students apply trigonometry to measure **tree and building heights, river widths, and ramp slopes** while moving between physical measurements, visual diagrams, and symbolic calculations. The Tier 2/Tier 3 structure, guided procedures, vocabulary supports, and visual representations make it especially useful for **RTI/MTSS, Algebra 1/Geometry support, Special Education, small-group intervention, and students who need stronger conceptual foundations in trigonometry**.
Product description
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 rather than abstract memorization.
### 📦 WHAT'S INSIDE (36 PAGES, PRINT & DIGITAL READY)
✅ **4 Hands-On Measurement Stations** — Each includes full procedure cards, data sheets, and exit tickets:
**Station 1: Tree Height with a Clinometer** — Build a clinometer using a protractor, straw, string, and washer, then use it to measure tree height.
**Station 2: Building Height via Shadows & Similar Triangles** — Apply shadows and similar triangles to determine building height.
**Station 3: River Width** — Measure river width using only a tape measure and a straw. The activity can be set up in a hallway, so no actual river is needed.
**Station 4: Ramp Slope** — Use a tangent ratio and a free inclinometer phone app, including an ADA compliance check.
✅ **Explicit Vocabulary Pre-Teaching with Visual Anchors** — Opposite, adjacent, hypotenuse, angle of elevation, and angle of depression
✅ **SOH-CAH-TOA Concept Refresher** — Includes 2 fully worked examples
✅ **I Do / We Do / You Do Procedure Cards** — Gradual-release support for every station
✅ **Detailed Solutions** — Step-by-step solutions for every exit ticket and worked example
✅ **Tier 3 Modified Version** — Sin and cos only, with calculator-supported frames for students needing additional scaffolding
✅ **Error-Correction Protocol** — Identify → Re-teach → Re-practice → Re-assess, plus 6 common trig errors with targeted fixes
✅ **Student Reflection + Real-World Trig Careers Page** — Includes surveyor, civil engineer, architect, navigator, and more
✅ **Full Answer Key**
### 🧠 WHY THIS UNIT WORKS FOR RTI TIER 2
Students who struggle with abstract trigonometry instruction may have difficulty deciding whether to use **sin, cos, or tan**. This unit addresses that challenge through a **concrete → representational → abstract** sequence:
**Concrete:** Students physically measure with a tape **Representational:** Students label a diagram **Abstract:** Students compute using a trigonometric ratio
Each station uses a real-world indirect-measurement context drawn from surveying.
### 📐 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 & FORMAT
**Grades:** 9–11 **Duration:** 3–5 days **Format:** PDF (print & digital) **Pages:** 36
### 🛠 MATERIALS YOU'LL NEED
Protractors Straws String Washers Tape measures Calculators A free inclinometer phone app for Station 4
Frequently Asked Questions
What grades is this PBL unit designed for?
It is designed for **Grades 9–11**.
How long does the unit take?
The unit is designed for **3–5 days**.
How many measurement stations are included?
There are **4 hands-on measurement stations** covering tree height, building height, river width, and ramp slope.
Do students build a clinometer?
Yes. Station 1 includes instructions for building a clinometer from a **protractor, straw, string, and washer**.
Does the river-width activity require an actual river?
No. The description specifically states that Station 3 can be **set up in a hallway** using a tape measure and straw.
What trigonometry concepts are covered?
The unit includes **SOH-CAH-TOA, opposite/adjacent/hypotenuse, angles of elevation and depression, and applied trigonometric ratios**.
Are worked examples and answer keys included?
Yes. The resource includes **2 fully worked SOH-CAH-TOA examples, detailed solutions for exit tickets and worked examples, and a full answer key**.
Is additional scaffolding included?
Yes. The unit includes **I Do / We Do / You Do procedure cards, visual vocabulary anchors, a Tier 3 modified version, and an error-correction protocol**.
What is included in the Tier 3 version?
The Tier 3 version focuses on **sine and cosine only** and includes **calculator-supported frames**.
Is a phone app required?
Only for **Station 4**, which uses a free inclinometer phone app.
What standards are addressed?
The unit lists **CCSS HSG-SRT.C.6, HSG-SRT.C.8, and HSG-SRT.B.5**.
