an 18-foot ladder leans against the wall of a building. the base of the ladder is 9 feet from the bulding on level ground.how many feet up the wall,to the nearest tenth of a foot,is the ladder?

The ladder forms the hypotenuse of a right triangle. Solve for a

a^2 + b^2 = c^2
a^2 + 9^2 = 18^2
a^2 + 81 = 324
a^2 = 243
a = 15.589 = 15.6 feet

Well, it seems like this ladder has some lofty aspirations! To figure out how many feet up the wall it reaches, we can use a classic mathematical tool known as the Pythagorean theorem. According to this theorem, if we have a right triangle formed by the ladder, the ground, and the wall, the square of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides.

So, in this case, we have the base of the ladder (9 feet) and the length of the ladder (18 feet). To find the height up the wall, we'll let "x" represent that unknown length. Using the Pythagorean theorem, we can equate the squares of the ladder length and the two sides of the triangle:

9^2 + x^2 = 18^2

Simplifying this equation, we get:

81 + x^2 = 324

Now, let's bring out our math skills and solve for "x." Subtracting 81 from both sides:

x^2 = 243

Now, let's take the square root of both sides:

x ≈ 15.6 feet

So, to the nearest tenth of a foot, the ladder reaches approximately 15.6 feet up the wall. Let's hope it has a head for heights!

To find out how many feet up the wall the ladder reaches, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and its length is given as 18 feet. The base of the ladder is 9 feet from the building.

Let's call the height up the wall "h." We can set up the equation as follows:

h^2 + 9^2 = 18^2

Simplifying the equation, we have:

h^2 + 81 = 324

Subtracting 81 from both sides, we get:

h^2 = 243

Taking the square root of both sides, we find:

h ≈ √243

Using a calculator, we can determine that the square root of 243 is approximately 15.6.

Therefore, the ladder reaches approximately 15.6 feet up the wall, to the nearest tenth of a foot.

To find out how far up the wall the ladder reaches, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the ladder forms the hypotenuse of the triangle, while the base on the ground and the height up the wall form the other two sides.

Let's denote the height up the wall as 'h'.

Now, using the Pythagorean theorem, we have:

(9 feet)^2 + h^2 = (18 feet)^2

Simplifying this equation, we get:

81 + h^2 = 324

Subtracting 81 from both sides, we have:

h^2 = 243

To isolate 'h', we take the square root of both sides:

√(h^2) = √243

Simplifying further, we have:

h = √243

Using a calculator, we find that √243 is approximately 15.6 feet.

Therefore, the ladder reaches approximately 15.6 feet up the wall.