A - 12 ladder leans against the side of a house. The bottom of the ladder is 9ft from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth.

This looks like a job for the Pythagorean Theorem because the ladder and the house form a right-angle triangle.

a^2 + b^2 = c^2
9^2 + b^2 = 12^2
81 + b^2 = 144
b^2 = 63
b = ______

To solve this problem, you can use the Pythagorean theorem, which states that in a right-angled 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 is the hypotenuse, and the distance from the side of the house to the bottom of the ladder is one of the legs of the right triangle.

Let's denote the length of the ladder (hypotenuse) as c, the distance from the side of the house to the bottom of the ladder as a, and the height from the ground to the top of the ladder as b.

According to the Pythagorean theorem, we have the equation:

a^2 + b^2 = c^2

Substituting the given values:

9^2 + b^2 = 12^2

81 + b^2 = 144

Now, we can solve for b by subtracting 81 from both sides:

b^2 = 144 - 81

b^2 = 63

To find b, we need to take the square root of both sides:

b = √(63)

b ≈ 7.9

Therefore, the top of the ladder is approximately 7.9 feet from the ground.

To solve this problem, we can use the Pythagorean Theorem, which 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 side of the house and the ground. Let's call the distance from the ground to the top of the ladder "h" (the height we're trying to find).

According to the problem, the bottom of the ladder is 9 ft from the side of the house. This forms the base of our right triangle.

Using the Pythagorean theorem, we have:

(9^2) + (h^2) = A^2

Where A represents the length of the ladder (12 ft in this case).

Now, let's solve for h:

Simplify the equation:

81 + h^2 = 144

Subtract 81 from both sides:

h^2 = 144 - 81

h^2 = 63

Now, take the square root of both sides:

√(h^2) = √63

h ≈ 7.9 ft

Therefore, the top of the ladder is approximately 7.9 feet from the ground.