Loading…
Example 8.80 from Elementary Algebra, 8.7 Solve Proportion and Similar Figure Applications
Solve Proportion and Similar Figure Applications: example 8.80
Tyler is 6 feet tall. Late one afternoon, his shadow was 8 feet long. At the same time, the shadow of a tree was 24 feet long. Find the height of the tree.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
Read the problem and draw a figure. We are looking for h, the height of the tree. We will use similar triangles to write an equation. The small triangle is similar to the large triangle. Solve the proportion. Simplify. Check. Tyler's height is less than his shadow's length so it makes
sense that the tree's height is less than the length of its shadow.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
A telephone pole casts a shadow that is 50 feet long. Nearby, an 8 foot tall traffic sign casts a shadow that is 10 feet long. How tall is the telephone pole?
How did it go?