Question

Question
Scott is 6 feet tall and casts a shadow that is 8 feet long. A nearby tree is x feet tall and cast a show that is x+5 feet long.

How tall is the tree?

How long is the trees shadow?

Tree height:
feet

Tree shadow:
feet

Answer 1

To find the height of the tree and the length of its shadow, we can set up a proportion based on the similar triangles formed by Scott and the tree.

Scott's height and shadow give us:

\[
\frac{\text{Height of Scott}}{\text{Length of Scott's Shadow}} = \frac{\text{Height of Tree}}{\text{Length of Tree's Shadow}}
\]

Plugging in the values we know:

\[
\frac{6 \text{ feet}}{8 \text{ feet}} = \frac{x \text{ feet}}{x + 5 \text{ feet}}
\]

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

\[
6(x + 5) = 8x
\]

Expanding the left side:

\[
6x + 30 = 8x
\]

Now, rearranging the equation gives us:

\[
30 = 8x - 6x
\]

\[
30 = 2x
\]

\[
x = 15
\]

Now that we have the height of the tree:

**Tree height:** \(15\) feet

Next, we can find the length of the tree's shadow:

\[
\text{Length of Tree's Shadow} = x + 5 = 15 + 5 = 20 \text{ feet}
\]

Therefore:

**Tree shadow:** \(20\) feet

Final answers:

**Tree height:** 15 feet

**Tree shadow:** 20 feet