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On a softball field, 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.

A triangle is drawn on a baseball field. A point is at home plate, another point is at the pitcher apostrophe s mound, and another point is at an outfielder. The distance from home plate to the pitcher is 43 feet. The distance from home plate to the outfielder is 162 feet. The angle between the 2 sides is 27 degrees.

Law of cosines:

How far must the outfielder throw the ball to return it to the pitcher? Round to the nearest foot.

112 feet
125 feet
145 feet
156 feet

Sagot :

kaleighthompson2004

Answer: The answer is 125ft

Step-by-step explanation: I just did it

The law of cosines formula gives the square of the distance the

outfielder must throw the ball.

Correct response:

  • The distance the outfielder must throw the ball to return it to the pitcher is approximately 125 feet.

How to use the cosine rule to find the distance

Distance of the home plate from the pitcher's mound = 43 feet

Angle at which the ball is hit = 27° east of the pitcher's mound

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, a of the triangle is the distance from the outfielder to the pitcher.

According to 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

  • The distance the outfielder must throw the ball to return it to the pitcher is a ≈ 125 feet.

Learn more about the law of cosines here:

https://brainly.com/question/2491835

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