A 20 foot ladder is leaning aagainst a wall the base of the ladder is 7 feet away from the.wall hkw high up the wall will the ladder reacb

If you can imagine it, the figure will look like a right angle triangle. The hypotenuse will the 20 feet. The base will be 7 feet. The height is the unknown.

a^2 + b^2 = c^2
7^2 + b^2 = 20^2

Solve for 'b' and you will get the height of the wall where the ladder reaches.

To find out how high up the wall the ladder will reach, you can use the Pythagorean theorem, which is a mathematical formula that relates the lengths of the sides of a right triangle. In this case, the ladder acts as the hypotenuse, the wall acts as one of the legs, and the distance from the base of the ladder to the wall acts as the other leg.

The Pythagorean theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). Mathematically, it is written as:

c^2 = a^2 + b^2

In our scenario, the ladder is the hypotenuse (c), and the base of the ladder to the wall is one leg (a). The other leg, which represents the height the ladder will reach on the wall, is what we need to find (b).

Given that the base of the ladder is 7 feet away from the wall and the ladder is 20 feet long, we can substitute these values into the equation:

20^2 = 7^2 + b^2

Simplifying the equation:

400 = 49 + b^2

Subtracting 49 from both sides:

400 - 49 = b^2

351 = b^2

To solve for b, we take the square root of both sides:

√351 = √b^2

Approximately:

b = 18.733

Therefore, the ladder will reach approximately 18.733 feet up the wall.