1. Module 6

1.18. Page 3

Mathematics 10-3 Module 6: Lesson 4

Module 6: Triangles and Other Polygons

 

Explore

 

In the previous lesson you explored the principles behind similar triangles. In particular, you investigated similar right triangles. In this activity you will explore how those principles are applied to solve a practical problem.

 

Try This

 

Work with a partner, if possible.

 

This photograph shows a tree and the shadow the tree casts on the ground.

iStockphoto/Thinkstock

 

You will use the same technique from the Get Started section to find the height of an object. Use a measuring tape for required measurements.

 

Step 1: Go outside when the sun is shining and, along a flat horizontal stretch of ground, measure the length of the shadow of a tall tree, a building, a vertical pole, or some other similar object the height of which is unknown.

 

Step 2: Measure the height of a short vertical object, such as a fence post, that casts a shadow along a level stretch of ground. Also, measure the length of this object’s shadow along the ground.

 

Next, answer these questions to determine the height of the object in Step 1.

 

TT 1. Draw a diagram consisting of two similar right triangles, much like the diagram in Get Started.

 

TT 2. How do you know the two right triangles in your diagram are similar?

 

TT 3. Set up a proportion, and then solve for x.

 

TT 4. Is your answer to TT 3 reasonable? Explain your answer.

 

Share

 

In the Get Started and Explore sections, you saw two examples of right triangles that are similar. Are all right triangles similar? Try drawing a pair of right triangles that are not similar. Can you actually draw two right triangles that are not similar? Why or why not?

 

Share your ideas and any drawings with a partner, a group, or a facilitator.

 

Summarize your answers to these Share questions, and place a copy in your course folder. Also include your answers to TT 1 to TT 4.