Hi! I'd be happy to help you with your question. To find the height of the top of the ladder from the ground, we need to use the Pythagorean theorem, which involves the terms "ladder" (hypotenuse), "distance from the house" (base), and "height from the ground" (height).
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the ladder, in this case) is equal to the sum of the squares of the other two sides (base and height). So, we have:
ladder^2 = base^2 + height^2
Given that the ladder is 11 ft long and the base (distance from the house) is 7 ft, we can plug these values into the equation:
11^2 = 7^2 + height^2
Now, solve for the height:
121 = 49 + height^2
Subtract 49 from both sides:
72 = height^2
Take the square root of both sides:
height = √72 ≈ 8.5 (rounded to the nearest tenth)
So, the top of the 11-ft ladder is approximately 8.5 ft high from the ground when it leans against the side of the house with its base 7 ft from the house.