Question

A tree that is 15 feet tall casts a shadow that is 4 feet long. What is the distance from the top of the tree to the tip of the shadow? Round to the nearest tenth.

15.5 feet
12.1 feet
3.9 feet
2.0 feet

Answer 1

To find the distance from the top of the tree to the tip of the shadow, we can use the Pythagorean theorem.

The scenario involves a right triangle where:
- One leg is the height of the tree (15 feet).
- The other leg is the length of the shadow (4 feet).
- The hypotenuse is the distance from the top of the tree to the tip of the shadow.

Let \( d \) be the distance from the top of the tree to the tip of the shadow. According to the Pythagorean theorem:

\[ d^2 = \text{height}^2 + \text{shadow length}^2 \]

Substituting the values:

\[ d^2 = 15^2 + 4^2 \]
\[ d^2 = 225 + 16 \]
\[ d^2 = 241 \]

To find \( d \), we take the square root of 241:

\[ d = \sqrt{241} \]

Calculating that gives:

\[ d \approx 15.5 \text{ feet} \]

Thus, the distance from the top of the tree to the tip of the shadow is approximately **15.5 feet** (rounded to the nearest tenth).