Trigonometry Project

Trigonometry is all around us! Right triangles can be found in many daily situations. In this project, you will apply your knowledge of trigonometry to shadows in order to calculate the angle of elevation to the sun at different times of day.

To calculate the angle of elevation to the sun, use the following procedure:

·  Measure your height and the length of the shadow you cast at two different times of day (at least 3 hours apart)

·  Record the times and measurements (with units – to the nearest inch)

·  Draw the right triangle for each scenario / time of day

·  Label the sides of each drawing with your measurements and angle of elevation

·  Solve for the angle of elevation for each time of day while clearly showing all of your steps

Once you have completed the above procedure, answer the following questions in complete sentences:

  1. Explain the right triangle drawings you used to model each shadow scenario. Make sure your response answers the following:
  2. What does each side length represent? In particular, what does the hypotenuse in your drawing represent in the real world?
  3. From your measurements, when was your shadow the longest? What was the angle of elevation of the sun at this time?
  4. From your measurements, when was your shadow the shortest? What was the angle of elevation of the sun at this time?
  5. During what time of day do you think the shadow you cast will be the longest? Explain why using your knowledge of trigonometric ratios. (Make sure you mention the angle of elevation, your height, and a trig ratio that will help explain why the shadow is longest at this time of day.)
  6. During what time of day do you think the shadow you cast will be the shortest? Explain why using your knowledge of trigonometric ratios. (Use the hint from above, except you are explaining why the shadow at this time of day is shortest.)

What you will submit:

§  This rubric

§  ___ / 10 Tables of your height, shadow length (with units), and time of day (each table is 5pts)

§  ___ / 10 Two right triangle drawings (each drawing is 5 pts)

§  ___ / 5 Drawings labeled with your measurements and the angle of elevation (5 pts)

§  ___ / 10 Correct trig ratio used (10 pts)

§  ___ / 15 Show all steps and calculations when solving for the angle of elevation (15 pts)

§  ___ / 50 Answers to questions #1-5 (each question worth 10 pts)

___ / 100 Final Grade