Question

you are told that in a billiards shot, the cue ball was shot at the eight - ball, which was 8 inches away. as a result, the eight - ball rolled into a pocket, which was 6 inches away. knowing that the angle made with the path of the cue ball and the resulting path of the eight - ball is larger than 90°, it can be determined that the original distance from the cue ball to the pocket was greater than inches.

Explanation:

Step1: Apply Pythagorean theorem

Let the distance from the cue - ball to the pocket be $d$. Since the path of the cue - ball and the eight - ball form a right - angle, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 8$ inches and $b = 6$ inches.

Step2: Calculate the hypotenuse

$d=\sqrt{8^{2}+6^{2}}=\sqrt{64 + 36}=\sqrt{100}=10$ inches. Since the resulting path of the eight - ball is larger than 90 degrees, the original distance from the cue - ball to the pocket is greater than 10 inches.

Answer:

10