A billiard ball is struck by a cue. it travels 100 centimeters before ricocheting off a rail forming a 45 degree angle and traveling another 120 centimeters into a corner pocket. How far apart is the initial position of the ball from the corner pocket the ball was sunk in? Round answer to the nearest hundredth.
86
The correct answer is 86!
86
To find the distance between the initial position of the ball and the corner pocket, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the 100 centimeters traveled before ricocheting and the additional 120 centimeters traveled into the corner pocket form the two sides of the right triangle. We want to find the length of the hypotenuse, which represents the total distance traveled by the ball.
Using the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the hypotenuse and a and b represent the lengths of the other two sides.
In our case, let a = 100 and b = 120.
c^2 = 100^2 + 120^2
c^2 = 10000 + 14400
c^2 = 24400
Taking the square root of both sides, we find:
c ≈ √24400
c ≈ 156.08
Therefore, the distance between the initial position of the ball and the corner pocket is approximately 156.08 centimeters.
90
a^2 = b^2 + c^2 - 2bc x cosA
a^2 = 100^2 + 120^2 - 2(100)(120) x cos(45)
a^2 = 10,000 + 14,400 - 24,000 x cos(45)
square root of a^2 = square root of 11792.27227
a = 108.59