Final answer:
Using the Pythagorean theorem with the given lengths of the tent pole (10 feet) and distance from the pole (13 feet), we calculate the length of the rope to be approximately 16.4 feet.
Step-by-step explanation:
Ashley's scenario with the tent pole and rope forms a right triangle, where the tent pole is the vertical leg, the distance from the pole to where the rope is tied is the horizontal leg, and the rope is the hypotenuse. We can use the Pythagorean theorem to find the length of the hypotenuse (the rope), which states that a² + b² = c², where 'c' represents the length of the hypotenuse, and 'a' and 'b' are the lengths of the other two sides.
In this situation, the tent pole is 10 feet tall (a = 10 feet), and the rope is tied 13 feet from the pole (b = 13 feet). Plugging these values into the Pythagorean theorem:
a² + b² = c²
10² + 13² = c²
100 + 169 = c²
269 = c²
To find 'c', we take the square root of both sides:
c = √269
c ≈ 16.4 feet
Therefore, the length of the rope is approximately 16.4 feet.