a 10 foot ladder is leaning againts 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?
Strangely worded question . . .
2^2 + b^2 = 10^2
4 + b^2 = 100
b^2 = 96
b = 9.8
To find out how far up the building the ladder falls, we can use the concept of the Pythagorean theorem. Let me explain how you can solve this problem step by step:
1. Identify the given information:
- Length of the ladder (hypotenuse): 10 feet
- Distance of the ladder's base from the building (adjacent side): 2 feet
2. Use the Pythagorean theorem, which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b) of a right-angled triangle.
In this case, we can denote the distance up the building that the ladder falls as 'x' feet, making it the opposite side.
The equation for the Pythagorean theorem can be written as:
a^2 + b^2 = c^2
Plugging in the values we know:
2^2 + x^2 = 10^2
3. Solve the equation:
Simplify the equation:
4 + x^2 = 100
Subtract 4 from both sides:
x^2 = 100 - 4
x^2 = 96
Take the square root of both sides:
x = √96
Simplify the square root:
x ≈ 9.798 feet (rounded to three decimal places)
Therefore, the ladder falls approximately 9.798 feet up the building.