Question

On a sunny day, the tree in your backyard casts a shadow of 16 feet. At the same time, you cast a shadow of 4 feet. You are 5 feet 3 inches tall.

How tall is the tree?

17.3 ft
21 ft
21.2 ft
12.2 ft

Answer 1

To find the height of the tree using the proportionality of the heights and shadow lengths, we can set up a ratio based on the information given.

1. Convert your height from feet and inches to just feet.
- You are 5 feet 3 inches tall.
- There are 12 inches in a foot, so:
\[
3 \text{ inches} = \frac{3}{12} = 0.25 \text{ feet}
\]
- Therefore, your height in feet is:
\[
5 + 0.25 = 5.25 \text{ feet}
\]

2. According to the problem, your shadow is 4 feet long and the tree's shadow is 16 feet long. We can set up the following proportion:
\[
\frac{\text{Height of you}}{\text{Shadow of you}} = \frac{\text{Height of the tree}}{\text{Shadow of the tree}}
\]
Plugging in the known values:
\[
\frac{5.25}{4} = \frac{h}{16}
\]
Here, \(h\) represents the height of the tree.

3. Cross-multiplying to solve for \(h\):
\[
5.25 \times 16 = 4 \times h
\]
Calculating \(5.25 \times 16\):
\[
5.25 \times 16 = 84
\]
So we have:
\[
84 = 4h
\]
Dividing both sides by 4 gives:
\[
h = \frac{84}{4} = 21 \text{ feet}
\]

Thus, the height of the tree is **21 feet**.

So the correct answer from your options is **21 ft**.