A 13 foot ladder is leaning against a building.The bottom of the ladder is 5 feet from the building.How high up does the ladder meet the wall?
Use the Pythagorean Theorem.
a^2 + b^2 = c^2
a^2 + 5^2 = 13^2
a^2 + 25 = 169
a^2 = 169 - 25
a^2 = 144
a = 12
Well, this ladder seems to be quite the wallflower! If it's leaning against the building and the bottom is 5 feet away, we can use a little Pythagorean magic to find out where it meets the wall. So, let's put on our comedy cap and calculate:
When a 5-foot distance doesn't satisfy its need for attention, the ladder decides to reach out to the wall. By using the Pythagorean theorem (a^2 + b^2 = c^2), we can solve this equation for the height:
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 169 - 25
b^2 = 144
b = √144
b = 12
So, our ladder meets the wall approximately 12 feet above the ground. It's like the ladder thought, "Hey, wall, can we meet halfway?" And the wall was like, "Sure, buddy! 12 feet sounds perfect."
To find out how high up the ladder meets the wall, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, the distance from the building is one of the legs, and the height we're trying to find is the other leg.
Using the Pythagorean theorem, we have:
(Height of ladder)^2 + (Distance from building)^2 = (Length of ladder)^2
Let's substitute the given values into the equation:
(Height of ladder)^2 + (5 feet)^2 = (13 feet)^2
Simplifying the equation, we have:
(Height of ladder)^2 + 25 square feet = 169 square feet
Subtracting 25 square feet from both sides:
(Height of ladder)^2 = 169 square feet - 25 square feet
(Height of ladder)^2 = 144 square feet
Taking the square root of both sides to solve for the height of the ladder:
Height of ladder = sqrt(144 square feet)
Height of ladder = 12 feet
So, the ladder meets the wall at a height of 12 feet.
To determine how high up the ladder meets the wall, you 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 scenario, the ladder is the hypotenuse of the right triangle, the height of the wall is one of the sides, and the distance from the building to the ladder's bottom is another side.
Let's call the height of the wall "h" and the distance from the building to the ladder's bottom "d".
According to the question, the ladder is 13 feet long, and the bottom of the ladder is 5 feet from the building. In the right triangle, the ladder is the hypotenuse, so its length (13 feet) is equal to the square root of the sum of the squares of the other two sides:
13^2 = h^2 + d^2
Simplifying the equation:
169 = h^2 + 25
Now, let's isolate the variable "h":
h^2 = 169 - 25
h^2 = 144
To find the value of "h," we take the square root of both sides of the equation:
h = √(144)
h = 12 feet
Therefore, the ladder meets the wall at a height of 12 feet.