Using the shadow method, Norman finds the height of a tree as follows: He measures the shadow of the measuring stick (4ft) and the tree (20ft). He then uses similar triangles to find the tree's height.
If the measuring stick is 3 feet long, how tall is the tree?
4 feet squared + 20 feet squared = c squared
No hypotenuse is necessary. We are looking at corresponding sides of similar triangles here
3/4 = h/20
so
4 h = 4 * 5 *3
h = 15
Here is a picture of a similar (no pun intended) problem
http://mathforum.org/sanders/connectinggeometry/ch_09Similar.html
To find the height of the tree using the shadow method, Norman used the concept of similar triangles. Here's how you can do it:
1. First, determine the length of the measuring stick. In this case, the measuring stick is given to be 3 feet long.
2. Measure the length of the shadow cast by the measuring stick. According to the question, the shadow of the measuring stick is 4 feet long.
3. Measure the length of the shadow cast by the tree. According to the question, the shadow of the tree is 20 feet long.
4. Now, we can set up the proportion between the lengths of the shadow and the objects themselves:
Length of Measuring Stick / Length of its Shadow = Height of Tree / Length of Tree's Shadow
Using the given measurements, the proportion can be set up as:
3 feet / 4 feet = Height of Tree / 20 feet
5. Solve the proportion to find the height of the tree:
Cross-multiply to obtain:
3 feet * 20 feet = 4 feet * Height of Tree
60 feet = 4 feet * Height of Tree
Divide both sides of the equation by 4 feet:
60 feet / 4 feet = Height of Tree
Height of Tree = 15 feet
Therefore, the height of the tree is 15 feet.