Final answer:
To find the length of the rope, we apply the Pythagorean theorem to the right-angled triangle formed by the flagpole, the distance from the hook to the pole's base, and the rope. The length of the rope is calculated to be 50 feet.
Step-by-step explanation:
The question involves finding the length of a rope that runs from the top of a flagpole to a hook in the ground, given that the flagpole has a height of 30 feet and the hook is 40 feet from the base of the flagpole.
To solve this problem, we can 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 flagpole and the distance from the hook to the base of the pole form the two sides of a right-angled triangle, with the rope being the hypotenuse.
Let's call the length of the rope 'r'. We can set up the equation:
r^2 = 30^2 + 40^2
Solving for 'r', we do the following calculations:
1. Calculate the square of each side: 30^2 = 900 and 40^2 = 1600.
2. Add these values together: 900 + 1600 = 2500.
3. Find the square root of the sum to find the length of the rope: √2500 = 50.
Therefore, the length of the rope is 50 feet.