X-TREME Geometry!

Totally Intense Right Triangles!!

For this lesson you will need:

Ski Resorts Placemark (choose one):

1. New England Ski Resorts
2. Canadian Rockies Ski Resorts
3. Pacific West Ski Resorts
4. Sierra Nevada Ski Resorts
5. Colorado Ski Resorts

Scientific Calculator (free Mini-Calculator available here)

References on the Web - ThinkQuest Triangles , Trigonometric Table

For a complete Video Tutorial of each step, click here

Your Job: Find the most X-TREME Ski Run!

How to find the most X-Treme Run.

1. Download one of the placemarks above for the resort area you want to explore and open it with Google Earth.
2. In Google Earth, navigate to a resort area and visually inspect the runs. Find the one you think is most X-treme!
3. Find the beginning and ending elevations for the run.
4. Measure the straight-line length of the run.
5. Using a piece of paper or a word processing program or a draw program, calculate the following;
• The length of the third side of the triangle using the Pythagorian Theorum (a² + b² = c²)
• The perimeter of the triangle using the formulat a+b+c
• The angle of the triangle at the bottom of the run by using the formula (sin x² = height of the run/length of the run)
• The angle of the triangle at the top of the run using the formula (x + 90^o + the angle from the previous step = 180^o)
• Be sure to show your work!!!
6. Open a Drawing or Painting Program capable of exporting to .jpg format.
7. Draw and label a triangle with the measurements and calculations you made.
8. Save the drawing as a .jpg.
9. In Google Earth create a placemark at the starting point of the ski run.
10. In the placemark, insert the .jpg as an in-line image. Use the html code: <img src="TYPE THE PATH TO THE JPG FILE HERE">
11. Save your placemark as a .kmz to hand in to the teacher.
12. In Google Earth, find a different ski resort and repeat the steps above as time permits!

The Sharpest Angles, The Longest Runs, That's what makes for some X-TREME Geometry!!