By: Shelly B. Kaufmann
In the late afternoon, a person who is 6 feet tall casts a shadow 15 feet long. If the top of their shadow is at the same point on the ground as the top of the shadow of a 50 foot tree, how far is the man from standing from the base of the tree?
Try setting up a proportion to determine the length of the shadow of the tree.
x = 125
Next, subtract the length of the man’s shadow from x to determine how far the man is from the base of the tree.
The man is 110 feet from the tree!
Think about what you know about triangles. Think about standing on the ground and looking at your own shadow. What part of a triangle might your body be? What part of the triangle might your shadow be?
Does your body and shadow form an angle?
Use GSP to illustrate this problem. Use similar triangles to solve. Side ratios should be corresponding. Angle measures should be congruent.
Start the construction by drawing triangle ABC.
Choose a point on the hypotenuse which is line j. The point should be close to angle C. Label your new point D. Construct a perpendicular to line k. Establish a new point E at the intersection. Hide the line, highlight points D and E and construct only the segment.
Would you get the same results if you had draw two separate triangles instead of a triangle within a triangle?