Final answer:
To calculate the height of the house, you can use the Pythagorean theorem. The height of the house is approximately 41.9 feet.
Step-by-step explanation:
To calculate the height of the house, we can use the Pythagorean theorem. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the base of the house is one of the sides of the triangle, and the roof is the hypotenuse. So, we have:
Base^2 + Height^2 = Hypotenuse^2
Given that the base is 29 feet and the hypotenuse (roof) is 51 feet, we can substitute these values into the equation:
29^2 + Height^2 = 51^2
Solving for Height, we have:
Height^2 = 51^2 - 29^2
Height^2 = 2601 - 841
Height^2 = 1760
Taking the square root of both sides, we get:
Height = √1760
Using a calculator, we find that the height of the house is approximately 41.9 feet.