A guy wire reaches from the top of a 24 ft. pole to a point on the ground 8 ft. from the pole. Find the length of the wire.
Remember the Pythagorean Theorem for finding the length of a side of a right triangle?
a^2 + b^2 = c^2
(24 * 24) + (8 * 8) = c^2
576 + 64 = c^2
640 = c^2
25.3 = c
To find the length of the guy wire, 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.
In this case, the pole is the vertical side, the distance from the pole to the ground is the horizontal side, and the guy wire is the hypotenuse.
Let's denote the length of the guy wire as 'x'.
According to the Pythagorean Theorem, we then have:
x^2 = (24 ft)^2 + (8 ft)^2
Simplifying the equation, we get:
x^2 = 576 + 64
x^2 = 640
To find the value of 'x', we take the square root of both sides:
√(x^2) = √640
x = √640
Now we can calculate the length of the guy wire:
To find the length of the guy wire, we can use the Pythagorean theorem. The theorem 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.
In this case, the pole, the distance from the pole to the point on the ground, and the guy wire form a right triangle. The pole forms the vertical side of the triangle, the distance from the pole to the point on the ground forms the horizontal side, and the guy wire forms the hypotenuse.
Let's use the variables h for the height of the pole, d for the distance from the pole to the point on the ground, and w for the length of the guy wire.
From the given information, we have:
h = 24 ft (height of the pole)
d = 8 ft (distance from the pole to the point on the ground)
Now, we can use the Pythagorean theorem to find the length of the guy wire:
w^2 = h^2 + d^2
Substituting the given values:
w^2 = (24 ft)^2 + (8 ft)^2
w^2 = 576 ft^2 + 64 ft^2
w^2 = 640 ft^2
To find w, we take the square root of both sides of the equation:
w = √(640 ft^2)
w ≈ 25.3 ft
Therefore, the length of the guy wire is approximately 25.3 feet.