a zip lines steel cable is being constructed for a Reality television competition show. The high end of the zip line is attached to the top of a 50 foot pole while the lower end is anchored at ground level to a stake 50 feet from the base of the pole
To construct a zip line steel cable for the Reality television competition show, follow these steps:
Step 1: Determine the required length of the steel cable.
In this case, the distance between the top of the pole and the stake is given as 50 feet. Therefore, the length of the steel cable should be approximately 50 feet.
Step 2: Ensure the pole's stability.
Make sure that the 50-foot pole is securely planted and can withstand the forces exerted by the zip line participants.
Step 3: Install the anchor at ground level.
Place a stake at the point that is 50 feet away from the base of the pole. The stake will serve as an anchor for the lower end of the steel cable.
Step 4: Attach the high end of the steel cable to the top of the pole.
Securely fasten one end of the steel cable to the top of the 50-foot pole. Ensure that the attachment is strong and stable.
Step 5: Connect the lower end of the steel cable to the anchor.
Attach the other end of the steel cable to the stake at ground level, which is located 50 feet away from the base of the pole. Ensure that the connection is secure and properly tightened.
Step 6: Test the tension and stability of the zip line.
Before allowing anyone to use the zip line, perform thorough testing to ensure the tension and stability of the steel cable. It is crucial to verify that it can safely support the weight and force exerted by participants.
Step 7: Regularly inspect and maintain the zip line cable.
After installation, regularly inspect and maintain the steel cable, checking for any signs of wear, damage, or rust. This step is essential to ensure the ongoing safety and reliability of the zip line.
Following these steps will help ensure the construction of a safe and reliable zip line steel cable for the Reality television competition show.
To find the length of the zip line's steel cable, we can use the Pythagorean theorem, which 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 other two sides.
Here, the zip line forms a right triangle, with one side being the height of the pole (50 feet) and the other side being the distance from the base of the pole to the stake (50 feet). We want to find the length of the hypotenuse, which represents the length of the steel cable.
Using the Pythagorean theorem, we can calculate the length of the cable as follows:
Length of the cable² = (Height of the pole)² + (Distance from the base of the pole to the stake)²
Length of the cable² = 50² + 50²
Length of the cable² = 2500 + 2500
Length of the cable² = 5000
Length of the cable = √5000
Using a calculator, we can find that the square root of 5000 is approximately 70.71. Therefore, the length of the zip line's steel cable is approximately 70.71 feet.
To summarize the steps:
1. Identify the right triangle formed by the zip line, the pole, and the base-stake distance.
2. Use the Pythagorean theorem: length of the cable² = (height of the pole)² + (distance from the base of the pole to the stake)²
3. Substitute the values: length of the cable² = 50² + 50²
4. Calculate the sum: length of the cable² = 2500 + 2500
5. Simplify: length of the cable² = 5000
6. Take the square root of both sides to find the length of the cable.
I don't mind helping to find answers, but I resent having to provide the questions as well.
Draw a diagram
Review your basic trig functions, or at least the Pythagorean Theorem ...