a ladder 17 feet long is leaned up against a house, reaching a height of 15 feet. how far from the house is the base of the ladder?
Or if you recognize that the triangle formed is a 17-15-8 Pythagorean triple, you can easily guess that the third side is 8 ft.
To find the distance from the base of the ladder to the house, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle (which is the case here since the ladder forms a right angle with the ground), the square of the hypotenuse (the longest side, which is the ladder) is equal to the sum of the squares of the other two sides.
In this scenario, the ladder is the hypotenuse, and the height of the ladder (15 feet) is one of the sides. Let's call the distance from the base of the ladder to the house "x."
We can set up the equation as follows:
x^2 + 15^2 = 17^2
Simplifying the equation will give us:
x^2 + 225 = 289
Subtracting 225 from both sides:
x^2 = 289 - 225
x^2 = 64
Taking the square root of both sides (since we're looking for a positive value for x):
x = √64
x = 8
Therefore, the base of the ladder is 8 feet away from the house.
Use the Pythagorean theorem to find the other leg of this right triangle.
a^2 + 15^2 = 17^2