Does his corner measure 90° ?

Question

Ben is checking to see if his fence measures 90° at the corner. To do so he measures out 10 feet along the fence and places a stake marking it point A. He then goes back to the corner and measures out 15 feet along the fence in the other direction and places a stake marking it point B as shown in the figure below. Lastly, he measures the distance between points A and B and finds it to be 20 feet. Does his corner measure 90°?

Answer 1

If 10²+15² = 20², then the angle at the corner will be 90^o. If not, then the angle is not a right angle.

Here is a Desmos graph that uses the Law of Cosines (SSS) to ascertain the same:

desmos.com/calculator/h3k0n44so3