Question

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

Answer 1

c = 125 f

Explanation:

Let´s call points A ( home plate ) B (pitcher´s place ) and C ( outfielder place)

these three points form a triangle in which according to cosine law, one side of a triangle c can be calculated by the equation:

c² = a² + b² - 2a*b*cos∡a,b

a and b are the other sides of the triangle and ∡a,b is the angle between sides a and b

All distances are in feet then the distance between outfielder and pitcher (c) is in feet:

c² = (43)² + ( 162)² - 2*(43)*(162)*cos 27° cos 27° = 0,891

c² = 1849 + 26244 - 12413,4

c² = 15679,6

c = √15679,6

c = 125 f