A ladder leans against a brick wall, The top of the ladder touches the wall 10 feet from the ground. The ladder is 15 feet long. How far does the bottom of the ladder sit from the wall? Round to the nearest tenth.
Use the Pythagorean Theorem >> a^2 + b^2 = c^2
You know one leg is 10 and the hyptenuse is 15. Solve for the length of the other leg.
The Pathagorean Therim
a squared + b squared = c squared
It's a triangle.
a squared is the unknown-
Distance from wall =a squared
b squared is how high up the ladder is from the ground = 10'
c squared is the hypotenuse of the triangle = 15' long ladder
To find out how far the bottom of the ladder sits from the wall, 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, the distance from the ground to the top of the ladder is one side, and the distance from the bottom of the ladder to the wall is the other side.
Let's denote the distance from the bottom of the ladder to the wall as 'x'.
According to the Pythagorean theorem:
15^2 = x^2 + 10^2
Simplifying this equation:
225 = x^2 + 100
Rearranging the equation:
x^2 = 225 - 100
x^2 = 125
Now, to find the value of 'x', we take the square root of both sides:
x = √125
Using a calculator, we find that √125 is approximately 11.2.
Therefore, the bottom of the ladder sits approximately 11.2 feet from the wall.
To find the distance between the bottom of the ladder and the wall, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the ladder) is equal to the sum of the squares of the other two sides.
In our case, the ladder forms the hypotenuse of the right triangle, and the wall and the distance from the bottom of the ladder to the wall form the other two sides. Let's denote the distance from the bottom of the ladder to the wall as x.
According to the Pythagorean theorem, we have:
ladder^2 = wall^2 + x^2
Substituting the given values, we get:
15^2 = 10^2 + x^2
Simplifying further:
225 = 100 + x^2
To isolate x^2, we subtract 100 from both sides:
x^2 = 125
Now, to find x, we can take the square root of both sides:
x = √125
Calculating that, we find:
x ≈ 11.2 (rounded to the nearest tenth)
Therefore, the bottom of the ladder sits approximately 11.2 feet from the wall.