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).
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