A guy wire is attached to the top of a pole. The other end of the guy wire is staked in the ground 29 feet from the base of the pole. How tall is the pole, if the guy wire is 73 feet long? Round to the nearest tenth.
This calls for the Pythagorean Theorem.
a^2 + b^2 = c^2
29^2 + b^2 = 73^2
841 + b^2 = 5,329
b^2 = 4,488
b = 66.99 = 67 feet
To find the height of the pole, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the guy wire represents the hypotenuse of the right triangle, and the distance from the base of the pole to the stake represents one of the sides. Let's call the height of the pole "h" and the distance from the base to the stake "d."
We can set up the equation as follows:
h^2 = 73^2 - d^2
The distance from the base to the stake is given as 29 feet, so:
d = 29
Substituting the value of d in the equation:
h^2 = 73^2 - 29^2
h^2 = 5329 - 841
h^2 = 4488
To find the height of the pole, we take the square root of both sides of the equation:
h = √4488
h ≈ 67.0
Therefore, the height of the pole is approximately 67.0 feet.
To find the height of the pole, we can use the Pythagorean theorem. In this case, the guy wire acts as the hypotenuse of a right triangle, and the distance from the base of the pole to the staked end is one of the legs.
Let's call the height of the pole "h", the distance from the base to the staked end "d", and the length of the guy wire "g".
From the problem statement, we know that:
d = 29 feet
g = 73 feet
According to the Pythagorean theorem, the equation is:
h^2 + d^2 = g^2
Substituting the known values:
h^2 + 29^2 = 73^2
Simplifying the equation:
h^2 + 841 = 5329
Subtracting 841 from both sides:
h^2 = 4488
To find the height (h), we need to take the square root of both sides of the equation:
sqrt(h^2) = sqrt(4488)
h = sqrt(4488)
Using a calculator, we find that h ≈ 67.03 feet.
Therefore, the height of the pole is approximately 67.03 feet to the nearest tenth.