a wall is 5 m. a ladder is leaning against it, which is 3 m. express the height from the top of the ladder above the ground as a function of how far the foot of the ladder is from the base of the wall.
3^2= base^2+ height^2
base= sqrt (9-height^2)
To express the height from the top of the ladder above the ground as a function of how far the foot of the ladder is from the base of the wall, we can use the Pythagorean theorem.
According to the Pythagorean theorem, 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 base and the height from the top of the ladder above the ground).
We are given that the length of the ladder (which is the hypotenuse) is 3 m, and the length of the base (which is the distance from the foot of the ladder to the base of the wall) is 5 m. Let us denote the height from the top of the ladder above the ground as h.
Using the Pythagorean theorem, we can write the equation as:
3^2 = 5^2 + h^2
Simplifying, we have:
9 = 25 + h^2
Rearranging the equation to solve for h, we subtract 25 from both sides:
h^2 = 9 - 25
h^2 = -16
Since we cannot have a negative square root, this equation does not have a real solution. This indicates that the ladder cannot reach the top of the wall when the foot of the ladder is 5 m away from the base of the wall.