Question

During a baseball game, a batter hits a ball approximately 107 feet from home plate. the shortstop, who is standing 58 feet from third base, catches the ball. the diagram below represents this situation, where c represents the distance the ball traveled, and a represents the distance between the shortstop and third base. note: picture is not drawn to scale. in relation to the third base line, at what angle, a, did the batter hit the ball?

Answer 1

The angle at which the batter hit the ball is approximately 61.2 degrees.

Step-by-step explanation:

The angle at which the batter hits the ball can be determined using trigonometry. We can use the tangent function to find the angle, which is defined as the ratio of the opposite side to the adjacent side.

In this case, the opposite side is the distance the ball traveled (c) and the adjacent side is the distance between the shortstop and third base (a). So, we can use the equation tan(a) = c/a to find the angle a.

Using the given values, c = 107 feet and a = 58 feet, we can calculate the angle a as follows:

a = tan-1(c/a) = tan-1(107/58) ≈ 61.2 degrees