A 1313 -foot ladder is leaning against a building, with the base of the ladder 22 feet from the building.

How high up on the building will the top of the ladder reach?

The ladder goes up 1312.82 ft up the building.

Step-by-step explanation:

We will use the Pythagoras theorem which is:

a² + b² = c²

where

a is the height at which the ladder will go up the building b is the distance at which the base of the ladder is away from the building c is the length of the ladder

Therefore, since we want the height at which the ladder will go up (a),

we will rearrange the equation above to be

a² = c² - b²

a = √ (c² - b²)

a = √ ((1313) ² - (22) ²)

a = 1312.82 ft

Thus, the ladder goes up 1312.82 ft up the building.