Tom has a 15 foot ladder that he leaned against the wall of his house. Tom put the base of the ladder 3 feet away from the house. How far up The house is the top of the ladder?
Use the Pythagorean Theorem
To find out how far up the house the top of the ladder is, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 this case, the ladder is the hypotenuse, and the other two sides are the distance from the base of the ladder to the house and the distance from the top of the ladder to the ground.
Let's name the distance from the base of the ladder to the house as "a," and the distance from the top of the ladder to the ground as "b."
According to the theorem, we can write the equation as follows:
a^2 + b^2 = c^2
Where "c" represents the length of the ladder.
Now, we have the following values:
a = 3 feet (distance from the base of the ladder to the house)
c = 15 feet (length of the ladder)
Substituting these values into the equation, we get:
3^2 + b^2 = 15^2
Simplifying this equation, we have:
9 + b^2 = 225
Subtracting 9 from both sides, we get:
b^2 = 216
To find the value of "b," we need to take the square root of both sides:
√(b^2) = √(216)
b = √(216)
Using a calculator, we find that the square root of 216 is approximately 14.697.
Therefore, the distance from the top of the ladder to the ground, which is also the height of the ladder on the house, is approximately 14.697 feet.