A carpenter wants to use a 12-foot ladder to reach a window that's 10 feet high. Which formula would you use to determine how far to place the ladder from the base of the house?

Pythagorean Theorem

a^2 + b^2 = c^2

Hallie is trying to win the grand prize on a game show. Should she try her luck by spinning a wheel with 6 equal sections labeled from 1 to 6 and hope she gets a 5, or should she roll two number cubes and hope she gets the same number on both cubes? Explain

Hallie is trying to win the grand prize on a game show. Should she try her luck by spinning a wheel with 6 equal sections labeled from 1 to 6 and hope she gets a 5, or should she roll two number cubes and hope she gets the same number on both cubes? Explain

Hallie is trying to win the grand prize on a game show. Should she try her luck by spinning a wheel with 6 equal sections labeled from 1 to 6 and hope she gets a 5, or should she roll two number cubes and hope she gets the same number on both cubes? Explain

Hold on, let me consult with my ladder-wielding comrades. Ah, yes! The formula you need is the Pythagorean theorem, my friend. It's like a mathematical superhero that saves the day. Just square the height of the window (10 feet) and square the length of the ladder (12 feet). Then subtract the two and take the square root of that difference. Voila! You'll know exactly how far to place the ladder from the base of the house.

To determine how far to place the ladder from the base of the house, you can use the Pythagorean theorem. The formula is:

a^2 + b^2 = c^2

where:
- a represents the height of the window (10 feet)
- c represents the length of the ladder (12 feet)

To find b, which represents the distance to place the ladder from the base of the house, you need to rearrange the formula:

b = √(c^2 - a^2)

In this case, the formula to use would be:

b = √(12^2 - 10^2)

To determine how far to place the ladder from the base of the house, you can use the Pythagorean theorem. The Pythagorean theorem relates the lengths of the sides of a right triangle, where the square 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 the hypotenuse of a right triangle, with the window height being one of the legs. The other leg represents the distance between the base of the house and the ladder's placement.

To find this distance, you can use the equation:

distance^2 + window height^2 = ladder length^2

Let's plug in the given values:

distance^2 + 10^2 = 12^2

Simplifying:

distance^2 + 100 = 144

Subtracting 100 from both sides:

distance^2 = 44

Taking the square root of both sides, considering the positive solution since distance cannot be negative:

distance ≈ √44

Therefore, the formula you would use to determine how far to place the ladder from the base of the house is:

distance ≈ √44