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To solve this problem, we need to calculate the distance the pitcher must travel to pick up the ball.

### Problem Analysis:
1. The batter drops the ball along the first-base line, and it travels a distance of 44 feet at an angle of 27° from the base path (first-base line).
2. The distance from the pitcher's mound to home plate is 60.5 feet.
3. The baseball diamond is square-shaped, meaning the pitcher's mound, home plate, and bases form a known geometric structure.

### Approach:
This problem can be treated as a triangle problem, where:
- We have one side (44 feet) and one angle (27°).
- We need to find the distance from the pitcher's mound to the ball (hypotenuse of a right triangle).

Let's call:
- \( A = 60.5 \) feet (distance from the pitcher to home plate),
- \( B = 44 \) feet (distance from home plate to where the ball lands),
- Angle \( \theta = 27^\circ \).

We will use the **Law of Cosines** because we know two sides and the included angle:
\[
C^2 = A^2 + B^2 - 2 \cdot A \cdot B \cdot \cos(\theta)
\]
where:
- \( C \) is the distance the pitcher needs to travel to reach the ball.

### Calculation:
1. Substitute the values into the Law of Cosines:
   \[
   C^2 = 60.5^2 + 44^2 - 2 \cdot 60.5 \cdot 44 \cdot \cos(27^\circ)
   \]

2. Calculate \( C \) by taking the square root of the result.

I'll compute this next.The pitcher must travel approximately **29.2 feet** to pick up the ball.

Would you like a detailed breakdown of each step? Or do you have further questions?

Here are some related questions to expand on this problem:
1. How would the answer change if the angle was 45° instead of 27°?
2. If the ball rolled an additional 10 feet, how would that affect the distance the pitcher needs to travel?
3. Can you use trigonometric identities to solve similar problems without the Law of Cosines?
4. What would the result be if the pitcher's distance from home plate was different?
5. How does knowing the properties of a square field simplify calculations in baseball problems?

**Tip:** The Law of Cosines is particularly useful when you know two sides and the included angle of a triangle.

A batter in a baseball game drops a bunt down the first-base line. It rolls 44 ft at an angle of 27° with the base path. The pitcher's mound is 60.5 ft from home plate. How far must the pitcher travel to pick up the ball? (Hint: A baseball diamond is a square.)

Learn how to calculate the distance a pitcher must travel to pick up a bunt that rolls 44 feet at an angle of 27° with the base path in a baseball game. This problem covers geometry and trigonometry concepts, using the Law of Cosines for a real-world application in sports.

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