A 13-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 12 feet from the base of the building. How high up the wall does the ladder reach?
the wall, ladder and ground form a 5-12-13 Pythagorean right triangle
To determine how high up the wall the ladder reaches, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length 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 is the hypotenuse of the right-angled triangle. The base of the triangle is the distance from the base of the building to where the ladder is placed, which is 12 feet. The height of the triangle is the unknown distance up the wall.
Using the Pythagorean theorem, we can calculate the height of the triangle as follows:
Hypotenuse^2 = Base^2 + Height^2
13^2 = 12^2 + Height^2
169 = 144 + Height^2
Subtracting 144 from both sides, we get:
25 = Height^2
Taking the square root of both sides, we find:
Height = √25
Height = 5 feet
Therefore, the ladder reaches a height of 5 feet up the wall.
To find how high up the wall the ladder reaches, we can use the Pythagorean theorem, which states that in a right 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 ladder is the hypotenuse, the distance from the base of the wall to the bottom of the ladder is one of the other sides, and the height up the wall is the remaining side.
Let's assign variables to the different sides:
- The height up the wall is h.
- The distance from the base of the wall to the bottom of the ladder is 12 feet.
According to the Pythagorean theorem, we have the equation:
h^2 + 12^2 = 13^2
To solve for h, we can simplify the equation and solve for h:
h^2 + 144 = 169
h^2 = 169 - 144
h^2 = 25
h = √25
h = 5
Therefore, the ladder reaches a height of 5 feet up the wall.