Final answer:
Using the Pythagorean Theorem, the length of the zip line that forms a right-angled triangle with the ground is calculated as 25 meters when one side is 15 meters high and the other side is 20 meters long, horizontally.
Step-by-step explanation:
The student is asking to find the length of the zip line that Sarah must set up to form a right-angled triangle with the ground. To find the length of the zip line, we will use the Pythagorean Theorem which states that in a right-angled 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 scenario, the height of the anchor point in the tree represents one side of the triangle (15 meters), and the distance horizontally from this point represents the second side of the triangle (20 meters).
We can represent this mathematically as:
c2 = a2 + b2
where c is the length of the hypotenuse (the zip line), and a and b are the lengths of the other two sides.
Substituting the given values into the formula gives us:
c2 = 152 + 202
c2 = 225 + 400
c2 = 625
Taking the square root of both sides to solve for c we get:
c = √625
c = 25
Therefore, the zip line should be 25 meters long to the nearest meter.