What is the area of a right triangle?

Question

The ladder is 13 feet long and the base is 5 feet from the building. How high can the ladder be from the roof?

Answer 1

The height of the ladder forms one of the legs of the right triangle, the length of the ladder forming the hypotenuse (13 ft) and the distance from the base to the building forming the other leg (5 ft).

By the Pythagorean Theorem the height of the ladder will be sqrt(13^2 - 5^2) = 12 feet.

Answer 2

The ladder is 13 feet long and the base is 5 feet from the building. How high can the ladder be from the roof?

I am not sure that I understand the question, since I don't know how high the building is. However, I can tell you how to find how far from the ground the ladder will hit the building.

You have a right triangle with a base of 5 feet, the distance from the building to the bottom of the ladder, and a hypotenuse of 13 feet, the length of the ladder.

I recommend sketching the right triangle, using little cross hatches on the hypotenuse to represent the rungs of the ladder. Use the Pythagorean Theorem to find the height above the ground that the ladder hits the building, which we will call A.

5² + A² = 13²

I am sure that you can take it from there, Rose! Good luck with geometry!