The top of a ladder is leaning on a building at a point 12 feet above the ground; the bottom of the ladder is 5 feet from the base of the building. What is the length of the ladder?
a^2 + b^2 = c^2
12^2 + 5^2 = c^2
144 + 25 = c^2
169 = c^2
13 = c
Well, I hope the ladder isn't too shy, because it's about to be the star of the show! Now, let's do some ladder math, shall we?
We have a ladder leaning on a building, reaching a point 12 feet above the ground and the bottom of the ladder is 5 feet away from the building. So, we have a right triangle situation going on here.
Using the good old Pythagorean theorem (a^2 + b^2 = c^2), we can find the length of the ladder (c) by considering the height (a) and the distance from the building (b).
So, plugging in the values we have, we get:
a^2 + b^2 = c^2
12^2 + 5^2 = c^2
144 + 25 = c^2
169 = c^2
Taking the square root of both sides, we find that c = 13. So the length of the ladder is 13 feet.
And there you have it! The ladder is 13 feet long. Now, remember, always climb ladders carefully and try not to do any acrobatics unless you're a professional acrobat-bot like me!
To find the length of the ladder, 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 ladder acts as the hypotenuse, and the building and the ground act as the other two sides.
Let's designate the length of the ladder as 'L', the height of the building as 'H', and the distance from the bottom of the ladder to the building as 'D'.
According to the problem, the height of the building (H) is 12 feet, and the distance from the bottom of the ladder to the building (D) is 5 feet.
Now, let's substitute these values into the Pythagorean Theorem formula:
L^2 = H^2 + D^2
Plugging in the known values:
L^2 = (12 feet)^2 + (5 feet)^2
Simplifying:
L^2 = 144 square feet + 25 square feet
L^2 = 169 square feet
Taking the square root of both sides:
L = √169 square feet
L = 13 feet
Therefore, the length of the ladder is 13 feet.
To find the length of the ladder, we can use the Pythagorean theorem, which 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 problem, the ladder forms the hypotenuse of a right-angled triangle, with one side being the height of the building where it is leaning, and the other side being the distance from the base of the building to the ladder.
Let's denote the length of the ladder as 'L'. We know that the height of the building (the vertical side) is 12 feet, and the horizontal side (the distance from the base of the building to the ladder) is 5 feet.
Using the Pythagorean theorem, we can set up the equation:
L^2 = 12^2 + 5^2
Simplifying:
L^2 = 144 + 25
L^2 = 169
To find the length of the ladder, we need to take the square root of both sides:
L = √169
L = 13
Therefore, the length of the ladder is 13 feet.