A 12-foot ladder is leaning against a wall. The base of the ladder is 4 feet from the wall. How tall is the wall?

To calculate the height of the wall, you can use the Pythagorean theorem, which states that the square of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides.

In this case, the base of the ladder forms one side of the right triangle, and the height of the wall is the other side (let's call it "h"). Therefore, you can solve for "h" using the formula:

h^2 = (12^2) - (4^2)

Simplifying the equation:

h^2 = 144 - 16
h^2 = 128

To find the value of "h," we can take the square root of both sides:

h ≈ √128
h ≈ 11.31

So, the height of the wall is approximately 11.31 feet.

To determine the height of the wall, we can utilize the Pythagorean theorem. According to the theorem, in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this scenario, the ladder acts as the hypotenuse, and the base of the ladder and the height of the wall form the other two sides of the right triangle.

The base of the ladder is given as 4 feet, and the length of the ladder is 12 feet. Therefore, we can substitute these values into the Pythagorean theorem equation:

hypotenuse^2 = base^2 + height^2

12^2 = 4^2 + height^2

Simplifying the equation:

144 = 16 + height^2

Subtracting 16 from both sides:

144 - 16 = height^2

128 = height^2

Taking the square root of both sides:

√128 = √(height^2)

11.31 ≈ height

Therefore, the height of the wall is approximately 11.31 feet.

Two angles are supplementary.One angle measures 2 more than 3 times the other angle.what is the measure of each angle?

the wall, ground, and ladder form a righ triangle, with the ladder as hypotenuse, so,

x^2 + 4^2 = 12^2

supplementary angles add up to 180 degrees. So,

x + 3x+2 = 180

one angle is x, the other is 3x+2. Solve for x, and you're almost there.