how far up the wall is a 13 ft ladder, if the baseof the ladder is 8 feet away from the wall
To determine how far up the wall a 13-ft ladder reaches when the base is 8 feet away, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the ladder represents the hypotenuse, and the base and the height up the wall represent the other two sides of the triangle. The length of the ladder is given as 13 ft, and the distance of the base from the wall is 8 ft.
Using the Pythagorean theorem, we can set up the equation as follows:
hypotenuse^2 = base^2 + height^2
Substituting the given values, we have:
13^2 = 8^2 + height^2
Solving for the height:
169 = 64 + height^2
105 = height^2
Taking the square root of both sides, we get:
height ≈ √105
Calculating it further, we find:
height ≈ 10.247
Therefore, the ladder reaches approximately 10.247 feet up the wall.