A right angle can be established by measured distances when a laserplane, builders' level, or transit is not available. Which measurement correctly represents this scenario?

To determine if a right angle can be established using measured distances without a laser plane, builders' level, or transit, one can apply the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the provided measurements represent the two shorter sides of a right triangle:

• For the choice where the measurements are A=90 degrees, B=8'-0", and C=6'-0", we can calculate the hypotenuse as follows:

• B² + C² = 8² + 6² = 64 + 36 = 100

• D (the hypotenuse) is √100, which equals 10'-0".

This confirms that the measurements represent a right triangle, establishing a right angle.

The other sets of measurements do not provide a valid right triangle based on the Pythagorean theorem, meaning the calculations will not yield an integer or valid hypotenuse. Thus, only the measurements from the correct answer fit the criteria necessary to ensure a right angle can be reliably established.