If a painter has a ladder 20 feet long .How high will the ladder reach if he set the base 2 feet from the building?

19.8997487421324 ft

This 19 ft and around 10.8 inches.

You need to use the following rule about right angled triangles, that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse (the long side)

In this example, the hypotenuse is the ladder itself, resting at an angle against the wall. So the square of the ladder length is 400

You know that the base of the triangle is the distance from the wall (2 feet) which squared is 4.

Subtract 4 from 400 and you get 396. The square root of this is 19.9 feet or 19 feet and 10.8 inches.

However, note that a ladder should normally be placed at an angle of around 15 degrees from the vertical. A two foot base is too steep for safe use. See the discussion for more on this.

You calculate this using the following formula: