Bob needs to wash the windows on his house. He has a 25-foot ladder and places the base of the ladder 10 feet from the wall on the house. How far up the wall will the ladder reach?
a^2 + b^2 = c^2
10^2 + b^2 = 25^2
100 + b^2 = 625
b^2 = 525
b = 22.91 feet
To determine how far up the wall the ladder will reach, you can use the Pythagorean theorem. According to the theorem, 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 forms the hypotenuse of a right triangle, with the base of the ladder forming one of the sides and the distance up the wall being the other side. Let's call the distance up the wall "x."
So, we have:
Base of the ladder = 10 feet
The length of the ladder (hypotenuse) = 25 feet
The distance up the wall = x (unknown)
Now we can use the Pythagorean theorem to solve for x.
The equation is:
(Length of Ladder)^2 = (Base)^2 + (Height)^2
Substituting the values we have:
25^2 = 10^2 + x^2
625 = 100 + x^2
x^2 = 625 - 100
x^2 = 525
To find x, we take the square root of both sides:
x = √525
x ≈ 22.91
Therefore, the ladder will reach approximately 22.91 feet up the wall.
To find out how far up the wall the ladder will reach, we can use the Pythagorean theorem.
According to the Pythagorean theorem, in a right-angled triangle, the square 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 base of the ladder to the wall acts as one side, and the distance up the wall acts as the other side.
Let's label the sides of the triangle:
- The distance from the base of the ladder to the wall = a = 10 feet
- The distance up the wall = b (which we need to find)
- The length of the ladder = c = 25 feet
Using the Pythagorean theorem, we can write the equation as:
a^2 + b^2 = c^2
Substituting the given values:
10^2 + b^2 = 25^2
Simplifying:
100 + b^2 = 625
Subtracting 100 from both sides:
b^2 = 625 - 100
b^2 = 525
Taking the square root of both sides:
b = √525
Calculating the square root of 525 is approximately:
b ≈ 22.91
So, the ladder will reach approximately 22.91 feet up the wall.