A 15 foot ladder propped against a wall the base of the ladder is 3 feet from the wall how far up the wall does the ladder reach.
3^2 + h^2 = 15^2
To determine how far up the wall the ladder reaches, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this scenario, the ladder acts as the hypotenuse, the distance from the base of the ladder to the wall acts as one side (3 feet), and the distance up the wall that the ladder reaches acts as another side (let's call it "x" feet). We can set up the equation as follows:
x^2 + 3^2 = 15^2
Simplifying the equation:
x^2 + 9 = 225
Subtracting 9 from both sides:
x^2 = 216
Taking the square root of both sides:
x = √216 ≈ 14.6969
Therefore, the ladder reaches approximately 14.6969 feet up the wall.