Question

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?

Answer 1

The ladder goes up 1312.82 ft up the building.

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.