Final answer:
Using the Pythagorean theorem, the height of the right triangle-shaped house is found to be approximately 41.95 feet, given the base is 29 feet and the hypotenuse (roof) is 51 feet.
Step-by-step explanation:
The student is asking to calculate the height of a right triangle-shaped house, given the length of the roof (hypotenuse) and the base. This can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a^2 + b^2 = c^2.
Let's consider the base of the triangle as a = 29 feet, the hypotenuse as c = 51 feet, and we want to find the height, which we'll call b.
- First, square the lengths of the base and the hypotenuse: a^2 = 29^2 and c^2 = 51^2.
- Then, calculate the square of the base: 29^2 = 841.
- Next, calculate the square of the hypotenuse: 51^2 = 2601.
- Now, apply the Pythagorean theorem to find b^2: b^2 = c^2 - a^2.
- Subtract the square of the base from the square of the hypotenuse: 2601 - 841 = 1760.
- Finally, take the square root of 1760 to find the height b: √1760 ≈ 41.95 feet.
Therefore, the height of the house is approximately 41.95 feet.