The distance the outfielder must throw the ball to return it to the pitcher is 125 feet.
Given
On a softball field, the home plate is 43 feet from the pitcher’s mound.
A ball is hit at an angle of 27° east of the pitcher’s mound.
The ball travels 162 feet before it is caught by an outfielder.
<h3>How to use the cosine rule to find the distance?</h3>
Distance of the home plate from the pitcher's mound = 43 feet
The angle at which the ball is hit = 27° east of the pitcher's mound
The distance the ball travels before it is caught = 162 feet
The sides, b and c, and the included angle, A, of the triangle drawn are respectively;
b = 43 feet
c = 162 feet
A = 27°
The length of the third side, of the triangle, is the distance from the outfielder to the pitcher.
According to the law of cosines, we have;
a² = b² + c² - 2·b·c·cos(A)
a² = 43² + 162² - 2 × 43 × 162 × cos(27°) ≈ 15679.497105
Approximating to the nearest foot, we get;
a = 125 feet
Hence, the distance the outfielder must throw the ball to return it to the pitcher is 125 feet.
To know more about the Cosine rule click the link given below.
brainly.com/question/3240813
