Question

A zip-line is being installed. The higher end of the line is attached to the top of a 70 foot pole while the lower end is anchored at ground level to a stake 70 feet from the base of the pole. Find the angle of elevation for the sip-line and the amount of cable needed to make the zip-line.

Answer 1

We can use trigonometry to solve this problem.

Let's call the angle of elevation of the zip-line as "x"

We can use the tangent function to find the angle of elevation:

tan(x) = Opposite/Adjacent

Where opposite is the height of the pole (70 feet) and adjacent is the horizontal distance between the base of the pole and the stake (70 feet).

So we can write:

tan(x) = 70/70

As the adjacent and opposite sides are the same, the tangent of the angle is 1.

The angle of elevation of the zip-line is x = arctan(1) = 45 degrees

To find the amount of cable needed we can use the Pythagorean theorem, as we have a right triangle with the zip-line as the hypotenuse, the height of the pole as one leg, and the horizontal distance between the base of the pole and the stake as the other leg

The cable length is equal to the hypotenuse of the right triangle, which can be calculated as the square root of the sum of the squares of the other two sides:

cable length = √(70² + 70²) = √(4900 + 4900) = √(9800) = 99 feet

So the amount of cable needed to make the zip-line is 99 feet.