A 10-foot ladder is leaning against a wall. The base of the ladder is 2 feet from the base of the building. How far up the building does the ladder fall?
a^2 + b^2 = c^2
2^2 + b^2 = 10^2
4 + b^2 = 100
b^2 = 96
b = 9.7979589
To find out how far up the building the ladder falls, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, and the base of the ladder is one of the sides. We can use the formula and the given information to solve the problem step by step.
Step 1: Identify the given information:
- The height of the ladder (hypotenuse) = 10 feet
- The distance from the base of the ladder to the base of the building (one side) = 2 feet
Step 2: Apply the Pythagorean theorem:
According to the theorem, we have the equation: (hypotenuse)^2 = (side1)^2 + (side2)^2
In this case, side1 is 2 feet, and side2 is the height we need to find.
Substituting the values, we get:
(10)^2 = (2)^2 + (side2)^2
Simplifying, we have:
100 = 4 + (side2)^2
Step 3: Solve for side2:
Move 4 to the left side of the equation by subtracting it from both sides:
100 - 4 = (side2)^2
96 = (side2)^2
Now, take the square root of both sides to find side2:
√96 = √((side2)^2)
Approximately, 9.80 = side2
Therefore, the ladder falls approximately 9.80 feet up the building.