Question

Jacob is
feet tall and casts a shadow that is
feet long.
The two triangles formed are similar because the angle to the sun is the same.

What is the height of the tree?


A right triangle with height of a tree question mark and width 27 feet. A right triangle with height of a man 5 feet and width 4.5 feet.

Answer 1

To find the height of the tree using similar triangles, we can set up a proportion based on the information given.

Let's define the variables:
- Height of Jacob (the man) = 5 feet
- Length of Jacob's shadow = 4.5 feet
- Height of the tree = \( h \) (unknown)
- Length of the tree's shadow = 27 feet

Since the triangles are similar, we can set up the following proportion:

\[
\frac{\text{Height of Jacob}}{\text{Length of Jacob's shadow}} = \frac{\text{Height of the tree}}{\text{Length of the tree's shadow}}
\]

Substituting the known values into the proportion gives:

\[
\frac{5}{4.5} = \frac{h}{27}
\]

Now, we can cross-multiply to solve for \( h \):

\[
5 \cdot 27 = h \cdot 4.5
\]

\[
135 = 4.5h
\]

Next, solve for \( h \) by dividing both sides by 4.5:

\[
h = \frac{135}{4.5}
\]

Calculating \( \frac{135}{4.5} \):

\[
h = 30
\]

Thus, the height of the tree is **30 feet**.