a 26- foot wire reaches from the top of a pole to a stake in the ground. if the distance from the base of the pole to the stake is 10 feet, how high is the pole?
a^2 + b^2 = c^2
a^2 + 10^2 = 26^2
a^2 + 100 = 676
a^2 = 576
a = 24
let the height be h
solve for h:
h^2 + 10^2 = 26^2
To find the height of the pole, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled 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 wire represents the hypotenuse, the distance from the base of the pole to the stake represents one side, and the height of the pole represents the other side.
Let's call the height of the pole 'h'.
According to the Pythagorean theorem:
h^2 + 10^2 = 26^2
h^2 + 100 = 676
Subtract 100 from both sides:
h^2 = 576
To find the height, take the square root of both sides:
√(h^2) = √576
h = 24
Therefore, the height of the pole is 24 feet.
To find the height of the pole, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the height of the pole will be one of the sides of the right triangle, while the wire and the distance from the base of the pole to the stake will be the other two sides.
Let's label the height of the pole as 'h,' the distance from the base of the pole to the stake as 'a,' and the length of the wire as 'c.'
According to the Pythagorean theorem:
c^2 = a^2 + h^2
Given that the length of the wire (c) is 26 feet and the distance from the base of the pole to the stake (a) is 10 feet:
26^2 = 10^2 + h^2
Simplifying:
676 = 100 + h^2
Subtracting 100 from both sides:
576 = h^2
Taking the square root of both sides:
h = √576
h ≈ 24 feet
Therefore, the height of the pole is approximately 24 feet.