Introduction
Imagine you are a surveyor, architect, engineer, or construction manager. One of the most common challenges these professionals face is determining the height of objects that cannot be measured directly.
How tall is a water tower?
How high is a cell phone tower?
How tall is your school building?
Using right triangle trigonometry, professionals solve these problems every day without ever climbing the structure.
Your team has been hired by the City Planning Department to determine the heights of several structures using trigonometric principles.
Task
Your mission is to investigate how right triangle trigonometry is used in real-world careers and then use those skills to determine the heights of various objects.
You will:
- Research careers that use trigonometry.
- Learn how surveyors determine heights.
- Calculate unknown heights using trigonometric ratios.
- Collect measurements around campus.
- Create a report and presentation defending your calculations.
Process
Step 1: Research Trigonometry Careers
Investigate careers that use right triangle trigonometry.
Examples:
- Surveyor
- Civil Engineer
- Architect
- Construction Manager
- Pilot
- Military Navigator
For each career identify:
- Job duties
- Education requirements
- How trigonometry is used
Step 2: Learn the Mathematics
Review right triangle trigonometric ratios.
- Sine
- Cosine
- Tangent
Complete practice problems involving:
- Sine
- Cosine
- Tangent
Create a chart explaining when each ratio should be used.
Step 3: Become a Survey Team
Using a clinometer, phone app, or protractor clinometer:
Measure:
- Angle of elevation
- Distance from object
Possible objects:
- Flagpole
- School building
- Light pole
- Tree
- Stadium lights
Record measurements.
Step 4: Calculate Heights
Use trigonometry to determine unknown heights.
Example:
Distance from object = 50 feet
Angle of elevation = 38°
Calculate:
Height = 50 × tan(38°)
Show all work and explain the process.
Step 5: Compare Results
Research the actual height if available.
Answer:
- Was your estimate reasonable?
- What factors may have caused error?
- How could measurements be improved?
Step 6: Create Your Final Product
Prepare a presentation that includes:
- Career research
- Photos of measured objects
- Angle measurements
- Trigonometric calculations
- Height estimates
- Sources of error
- Reflection
Resources
Trigonometry Tutorials
Khan Academy Right Triangle Trigonometry
https://www.khanacademy.org/math/geometry/right-triangles-topic
CK-12 Trigonometry
Math is Fun Trigonometry
Surveying and Engineering Careers
Bureau of Labor Statistics
National Society of Professional Surveyors
American Society of Civil Engineers
Measurement Tools
Clinometer App Information
NOAA Surveying Resources
Evaluation
| Criteria | Excellent (4) | Good (3) | Developing (2) | Beginning (1) |
|---|---|---|---|---|
| Career Research | Thorough and accurate | Mostly complete | Some missing information | Limited information |
| Data Collection | Accurate measurements | Minor errors | Some missing data | Incomplete |
| Trigonometric Calculations | All correct | Few errors | Multiple errors | Incomplete |
| Analysis of Error | Insightful reflection | Good reflection | Basic reflection | Minimal reflection |
| Presentation | Professional and engaging | Organized | Some organization issues | Difficult to follow |
Score: ____ /20
Conclusion
Right triangle trigonometry is much more than a chapter in a geometry textbook. Engineers, surveyors, architects, and scientists use these concepts daily to solve problems involving distance, height, and angles.
Through this WebQuest, you used mathematical modeling, technology, measurement, and critical thinking to solve real-world problems just like professionals do.
Final Question: How accurate were your measurements, and would you trust your calculations if a building project depended on them?