Use the Law of Cosines to solve the problem.
On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 216 feet. The path of the ball makes a 34° angle with the line connecting the pitcher and the catcher, to the right of the pitcher’s mound. An outfielder catches the ball and throws it to the pitcher. How far does the outfielder throw the ball?
assessment question 4
(1 point)
Responses
207.4 ft
207.4 ft
224.3 ft
224.3 ft
169.3 ft
169.3 ft
198.7 ft
To solve this problem using the Law of Cosines, we will consider the triangle formed by the pitcher's mound, the home plate, and the point where the ball is caught by the outfielder.
Let x be the distance the outfielder throws the ball.
Using the Law of Cosines, we have:
x^2 = 60.5^2 + 216^2 - 2(60.5)(216)cos(34°)
Calculating this expression gives:
x^2 = 3670.25 + 46656 - 26106cos(34°)
x^2 = 50326.919
Taking the square root of both sides gives:
x = √50326.919
x ≈ 224.30
Therefore, the outfielder throws the ball approximately 224.3 feet.
Therefore, the correct answer is:
224.3 ft