The tree in Jacob's yard casts a shadow that is 27
feet long.
Jacob is 5
feet tall and casts a shadow that is 4.5
feet long.
The two triangles formed are similar because the angle to the sun is the same.
What is the height of the tree?
Using the concept of similar triangles, we can set up a proportion to find the height of the tree.
Let h be the height of the tree.
According to the given information:
Height of Jacob = 5 feet
Length of Jacob's shadow = 4.5 feet
Length of tree's shadow = 27 feet
So, the proportion can be set up as:
5/h = 4.5/27
Cross multiplying, we get:
5 * 27 = 4.5 * h
135 = 4.5h
h = 135 / 4.5
h = 30
Therefore, the height of the tree is 30 feet.