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?

1 answer

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.