Question

Rob, an architect, visits the site of a building he has designed. His design calls for the corners where each wall meets to be square at 90°. The project manager has placed stakes at each corner to guide workers in building the walls. He goes to one of the stakes and, using a laser measure, finds that the distance of one wall will be 27 meters and the other wall will be 36 meters. Then he measures the diagonal length and determines it to be 48 meters. What will he likely tell the project manager?

a-The stakes need to be adjusted to improve the wall support
b-The stakes need to be adjusted because the corner is less than 90
c-The stakes need to be adjusted because the corner is greater than 90
d-The stakes need to be adjusted to make them more level

Answer 1

Using the Pythagorean theorem, Rob finds that the theoretical hypotenuse should be 45 meters instead of the measured 48 meters, indicating that the corner angle is greater than 90°.OPTION C.

Step-by-step explanation:

The question involves determining whether the corner of the walls in the building design forms a right angle based on the measurements provided. According to the information given, Rob measures one wall to be 27 meters, the other wall to be 36 meters, and the diagonal to be 48 meters. To determine whether these measurements form a right angle at the corner, we can use the Pythagorean theorem, which states that in a right-angled triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse).

We calculate the theoretical hypotenuse using the measurements:
27 meters squared plus 36 meters squared equals 729 + 1296 = 2025. The square root of 2025 is 45 meters. Since Rob has measured the diagonal (hypotenuse) to be 48 meters, which is longer than the calculated 45 meters, this indicates that the corner is not a perfect right angle and is greater than 90°.

Thus, the answer Rob will likely tell the project manager is:

b-The stakes need to be adjusted because the corner is greater than 90°.