Session 8, Part B:
Similar Triangles

In This Part: The Mirror Trick | Similarity Tests | Measuring with Shadows

 Using shadows is a quick way to estimate the heights of trees, flagpoles, buildings, and other tall objects. To begin, pick an object whose height may be impractical to measure, and then measure the length of the shadow your object casts. Also measure the shadow cast at the same time of day by a yardstick (or some other object of known height) standing straight up on the ground. Since you know the lengths of the two shadows and the length of the yardstick, you can use the fact that the sun's rays are approximately parallel to set up a proportion with similar triangles. Because the sun's rays are parallel, the triangles are similar. Thus:

Problem B3

On a sunny day, Michelle and Nancy noticed that their shadows were different lengths. Nancy measured Michelle's shadow and found that it was 96 inches long. Michelle then measured Nancy's shadow and found that it was 102 inches long.

 a. Who do you think is taller, Nancy or Michelle? Why? b. If Michelle is 5 feet 4 inches tall, how tall is Nancy? c. If Nancy is 5 feet 4 inches tall, how tall is Michelle?

 Video Segment In today's professional world, there are many practical applications that rely on triangle similarity. One such application is in medicine, where similar triangles are used to calculate the position of radiation treatment for cancer patients. In this segment, Sandra John-Baptiste and Jason Talkington work with dosimetrist Max Buscher to calculate the position of radiation beams so as to avoid their overlap on the spinal cord. Can you think of any other applications of triangle similarity? If you are using a VCR, you can find the first of these segments on the session video approximately 21 minutes and 10 seconds after the Annenberg Media logo. The second part of this segment begins approximately 22 minutes and 23 seconds after the Annenberg Media logo.

Next > Part C: Trigonometry

 Session 8: Index | Notes | Solutions | Video