Question

On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 257 feet at an angle of 31° to the right of the pitcher’s mound. An outfielder catches the ball and throws it to the pitcher. Approximately how far does the outfielder throw the ball?
A. 174.2 ft
B. 183.0 ft
C. 207.5 ft
D. 147.2 ft

Answer 1

Answer:

Option C (207.5 feet)

Step-by-step explanation:

The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. This means that the angle is formed by the intersection of the lines. Therefore, cosine rule will be used to calculate the length of b. The cosine rule is:

x^2 = y^2 + z^2 - 2*y*z*cos(X).

Let x be the distance covered by the outfielder's throw, let y be the distance between the pitcher's mound and the home plate, let z be the distance covered by the batter's shot, and let X be the mentioned angle.

The question specifies that y=60.5 feet, X=31°, and z=257 feet. Plugging in the values:

x^2 = 60.5^2 + 257^2 - 2(60.5)(257)*cos(31°).

Simplifying gives:

x^2 = 43053.9184501 feet.

Taking square root on the both sides gives x = 207.5 feet (rounded to the one decimal place).

This means that the Option C is the correct choice!!!