A ladder 8ft long leans against a wall. It rests on the ground 2ft from the wall. How high on the wall does the ladder reach?

Use the Pythagorean Theorem. Let a = the height on the wall.

a^2 + b^2 = c^2
a^2 + 4 = 64
a^2 = 60
a = 7.75 feet

To find out how high on the wall the ladder reaches, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the distance from the wall and the height on the wall).

In this case, the ladder is the hypotenuse, and we know the length of the ladder (8ft) and the distance from the wall (2ft). Let's use the Pythagorean theorem to find the height on the wall:

1. The length of the ladder = 8ft.
2. The distance from the wall = 2ft.
3. Let's call the height on the wall "h".
4. According to the Pythagorean theorem: (length of the ladder)^2 = (distance from the wall)^2 + (height on the wall)^2

Plugging in the values, we have:
(8ft)^2 = (2ft)^2 + h^2
64ft^2 = 4ft^2 + h^2
60ft^2 = h^2

Taking the square root of both sides:
√(60ft^2) = √(h^2)
√60ft = h
7.746ft ≈ h

Therefore, the ladder will reach approximately 7.746ft high on the wall.