A ladder is leaning against a building. The distance from the building to the bottom of the ladder is 7 feet. The ladder is 25 feet long. How high up the building is the top of the ladder?

24 feet

Step-by-step explanation:

The ladder leaning against the building resembles a right triangle. So, we can use the Pythagorean Theorem.

The Pythagorean Theorem is:

Where a and b are the legs of the right triangle and c is the hypotenuse.

We know that the distance from the building is 7 feet. This means that the base is 7. So, we can substitute 7 into either a or b.

We know the ladder itself is 25 feet long. So, the hypotenuse is 25. Substitute that for c. Therefore:

We need to solve for b to figure out how high up the building is the top of the ladder. Evaluate the squares:

Subtract 49 from both sides:

Take the square root of both sides:

So, the top of the ladder is 24 feet up from the building.

And we're done!