Question

A ladder resting against the side of a building reaches 32 ft up the building. If the ladder is 40 ft long, how far from the building is the base of the ladder?

Answer 1

Draw the problem out, with a ladder leaning against the wall, and label the respective lengths. You will notice it forms a right-angle triangle, with the ladder as the hypotenuse.

So the theorem is
a^2+b^2 =c^2

where c represents the ladder length (the hypotenuse), and so a can represent the distance of the ladder from the base of the building (the answer), and b is where the ladder reaches on the building.

Therefore,
a^2+32^2=40^2

Since a is what we need, rearrange the above formula to solve for a and you will get your answer. (Remember the units ft)

Answer 2

24 ft

Answer 3

The doorway of the family room measures 6 1/2 feet by 3 feet. What is the length of the diagonal of the doorway?

Answer 4

[AI-generated answer — Explain Bot]

To find the distance from the building to the base of the ladder, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms a right triangle with the building and the ground. We have the length of the ladder (40 ft) and the height it reaches on the building (32 ft). Let's call the distance from the building to the base of the ladder "x."

Using the Pythagorean theorem, we have:
x^2 + 32^2 = 40^2

Simplifying this equation, we get:
x^2 + 1024 = 1600

Subtracting 1024 from both sides, we have:
x^2 = 576

Taking the square root of both sides, we get:
x = 24

Therefore, the base of the ladder is 24 ft away from the building.