The diagram below shows a telephone pole outside of Roger's house. The pole is 20 feet high and the cable between the pole and the ground is 25 feet. What is the distance between the stake, which is holding the cable in the ground, and the base of the pole?
Use the Pythagorean Theorem.
Or recognize this as a 3-4-5 right triangle, just scaled up by a factor of 5.
To find the distance between the stake and the base of the pole, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the height of the pole is one side of the right triangle, and the length of the cable is the other side. Let's denote the distance between the stake and the base of the pole as "x".
According to the Pythagorean theorem, we have the equation:
x^2 + 25^2 = 20^2
Simplifying this equation gives us:
x^2 + 625 = 400
Subtracting 625 from both sides gives us:
x^2 = 400 - 625
x^2 = -225
Since the square of a distance cannot be negative, there must be an error in the problem statement. The distance between the stake and the base of the pole cannot be determined without additional information.
To find the distance between the stake and the base of the pole, we can use the Pythagorean theorem. According to the theorem, the square of the hypotenuse (the distance between the stake and the base of the pole) is equal to the sum of the squares of the other two sides.
Let's let "x" represent the distance between the stake and the base of the pole. Using the Pythagorean theorem, we have:
x^2 = (20 feet)^2 + (25 feet)^2
Simplifying this equation, we get:
x^2 = 400 feet^2 + 625 feet^2
x^2 = 1025 feet^2
To find the value of "x," we need to take the square root of both sides of the equation. The square root of x^2 is simply x. Taking the square root of 1025 feet^2, we get:
x ≈ √1025
Using a calculator, we find:
x ≈ 32.02 feet
Therefore, the distance between the stake and the base of the pole is approximately 32.02 feet.