A cable 25 feet long runs from the top of a utility pole to a point on the ground 18 feet from the base of the pole. How tall is the utility pole?
Pythagorean Theorem:
a^2 + b^2 = c^2
18^2 + b^2 = 25^2
324 + b^2 = 625
b^2 = 625 - 324
b^2 = 301
b = 17.349
Well, it seems like the cable is playing a little game of "hide and seek" with us. Let's use some good old Pythagoras to help us out here.
According to Pythagoras, in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the cable acts as the hypotenuse, and we have the two sides: the height of the pole (let's call it "h") and the distance from the base of the pole to the point on the ground (18 feet).
So, using Pythagoras' theorem, we can say that:
h^2 + 18^2 = 25^2
Now, let me get my math hat on. *puts on clown wig* It's time to solve this equation.
First, we'll square the numbers:
h^2 + 324 = 625
Then, we'll subtract 324 from both sides:
h^2 = 301
Now, let's find the square root of both sides to solve for "h":
h ≈ √301
And, drumroll, please...
After consulting my calculator... *drumroll intensifies*
The height of the utility pole is approximately 17.32 feet.
So, there you have it, my friend. The pole has revealed its height and we can now appreciate its tallness.
To find the height of the utility pole, we can use the Pythagorean theorem, which states that for a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's label the height of the pole as "h" and the base as "b".
According to the given information, the length of the cable (the hypotenuse) is 25 feet, and the distance from the base of the pole to the ground is 18 feet.
Using the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the length of the cable, a is the height of the pole, and b is the distance from the base of the pole to the ground.
Substituting the given values:
25^2 = a^2 + 18^2
625 = a^2 + 324
Rearranging the equation:
a^2 = 625 - 324
a^2 = 301
Taking the square root of both sides:
a = sqrt(301)
a ≈ 17.32
Therefore, the height of the utility pole is approximately 17.32 feet.
To find the height of the utility pole, we can use the Pythagorean theorem, which 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 pole, the ground, and the cable form a right triangle. The cable represents the hypotenuse, the distance from the base of the pole to the point on the ground represents one of the legs, and the height of the pole represents the other leg.
Let's assign variables to the different sides of the triangle:
- Hypotenuse (cable): c = 25 feet
- One leg (distance from base to point on the ground): a = 18 feet
- Other leg (height of the utility pole): b = ?
According to the Pythagorean theorem, we have the equation:
a^2 + b^2 = c^2
Substituting the known values:
18^2 + b^2 = 25^2
324 + b^2 = 625
b^2 = 625 - 324
b^2 = 301
Taking the square root of both sides:
b ≈ √301
Using a calculator, we find that b ≈ 17.32 feet.
Therefore, the utility pole is approximately 17.32 feet tall.