While working on the roof of his house, John leans a 15 foot ladder against a second story window. If the distance on the ground between the base of the ladder and the house is nine feet, at what height does the ladder reach the second story window? In your final answer, include all necessary calculations.

Question

While working on the roof of his house, John leans a 15 foot ladder against a second story window. If the distance on the ground between the base of the ladder and the house is nine feet, at what height does the ladder reach the second story window? In your final answer, include all necessary calculations.

Answer 1

a^2 + b^2 = c^2

9^2 + b^2 = 15^2

81 + b^2 = 225

b^2 = 144

b = 12 feet

Answer 2

a^2 + b^2 = c^2

9^2 + b^2 = 15^2

81 + b^2 = 225

b^2 = 144

b = 12 feet

Answer 3

To find the height at which the ladder reaches the second-story window, we can use the Pythagorean theorem, which states that for a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Let's label the height at which the ladder reaches the window as 'h', and the distance on the ground between the base of the ladder and the house as 'b'. The length of the ladder is given as 15 feet.

We can set up the following equation using the Pythagorean theorem:

b^2 + h^2 = 15^2

Substituting the given values:

9^2 + h^2 = 15^2

81 + h^2 = 225

Now, we can solve for 'h'. Subtracting 81 from both sides:

h^2 = 144

Taking the square root of both sides:

h = √144

h = 12

Therefore, the ladder reaches a height of 12 feet at the second-story window.

Answer 4

To find the height at which the ladder reaches the second-story window, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, 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 acts as the hypotenuse, and the distance on the ground and the height to the second-story window form the other two sides.

Let's denote the height as "h" and the distance on the ground as "d." We have the following information:

Base of the ladder to the house = 9 feet (d)
Length of the ladder = 15 feet

Applying the Pythagorean theorem, we have:

d^2 + h^2 = 15^2

Since we know the value of "d" as 9 feet:

9^2 + h^2 = 15^2

Simplifying:

81 + h^2 = 225

Subtracting 81 from both sides:

h^2 = 144

Taking the square root:

h = √144

h = 12 feet

Therefore, the ladder reaches a height of 12 feet at the second-story window.