Edwin needs to fix the window on the front of his house. The bottom of the window is 12 feet from the ground and he has a 13 foot ladder. How far from the base of the house should the ladder be to make a perfect right angle?

Answer 1

To solve this problem, we can use the Pythagorean theorem, which is applicable in right triangles. Here, the ladder acts as the hypotenuse, the height from the ground to the bottom of the window is one leg of the triangle, and the distance from the base of the house to the bottom of the ladder is the other leg.

Let's denote:

• The height of the window (the vertical leg) = 12 feet
• The length of the ladder (the hypotenuse) = 13 feet
• The distance from the base of the house to the base of the ladder (the horizontal leg) = \( x \)

According to the Pythagorean theorem:

\[ \text{(hypotenuse)}^2 = \text{(vertical leg)}^2 + \text{(horizontal leg)}^2 \]

Substituting the values we have:

\[ 13^2 = 12^2 + x^2 \]

Calculating the squares:

\[ 169 = 144 + x^2 \]

Now, subtract 144 from both sides:

\[ 169 - 144 = x^2 \]

\[ 25 = x^2 \]

Next, take the square root of both sides to find \( x \):

\[ x = \sqrt{25} = 5 \]

Thus, the distance from the base of the house to the base of the ladder should be 5 feet.

Answer 2

positive?

Answer 3

Yes, the distance \( x \) from the base of the house to the base of the ladder is indeed positive. The calculation we performed indicates that \( x = 5 \) feet, which is a positive value. In the context of this problem, distances are always positive, as they measure space between two points.

So, the answer remains: Edwin should place the ladder 5 feet from the base of the house to create a perfect right angle with the ground.