A 15-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?
A 19
-foot
ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 13
feet from the base of the building. How high up the wall does the ladder reach?
To find out 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, and the distance from the base of the building to the bottom of the ladder is one of the other sides. Let's call the height we want to find "h".
Using the Pythagorean theorem, we can set up the equation:
h^2 + 12^2 = 15^2
Simplifying, we have:
h^2 + 144 = 225
Subtracting 144 from both sides, we get:
h^2 = 225 - 144
h^2 = 81
To solve for h, we take the square root of both sides:
√h^2 = √81
h = 9
Therefore, the ladder reaches a height of 9 feet up the wall.
To determine 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 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 problem, the ladder forms the hypotenuse of the right triangle, and the distance from the base of the building to the wall forms one side of the triangle. The height we want to find represents the other side of the triangle.
Let's denote the height of the ladder on the wall as 'h'. We know that the distance from the base of the building to the wall is 12 feet, and the length of the ladder is 15 feet.
Using the Pythagorean theorem, we can write the equation:
12^2 + h^2 = 15^2
Simplifying the equation, we have:
144 + h^2 = 225
h^2 = 225 - 144
h^2 = 81
Taking the square root of both sides, we find:
h = √81
h = 9
Therefore, the ladder reaches a height of 9 feet up the wall.
a^2 + b^2 = c^2
12^2 + b^2 = 15^2
144 + b^2 = 225
b^2 = 225 - 144
b = 9