A wire is stretched from the top of a 12-foot pole to a stake in the ground and then to the base of the pole. If a total of 20 feet of wire is needed, how far is the stake from the pole (the answer is NOT 16)
8 feet
Let x be the distance.
√(x^2 + 12^2) + x = 20
√(x^2 + 144) = 20 - x
x^2 + 144 = 400 - 40x + x^2
40x - 256 = 0
x = 6.4
To find the distance between the stake and the pole, we can use the Pythagorean theorem.
The Pythagorean 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 lengths of the other two sides.
In this case, the pole acts as the vertical side (height), and the wire acts as the hypotenuse. The wire also has to touch the ground and make up the horizontal distance. Let's assume the horizontal distance is x.
So, we have the equation:
12^2 + x^2 = 20^2
Simplifying the equation:
144 + x^2 = 400
Subtracting 144 from both sides:
x^2 = 400 - 144
x^2 = 256
Taking the square root of both sides:
x = √256
x = 16
Therefore, the distance between the stake and the pole is 16 feet.