Question

If a door has three points A,B,C with length AB=12ft, AC=16ft, and BC=20ft, is the angle at A a right angle?

Answer 1

Since the largest side corresponds to the hypotenuse of a right triangle, we can draw the following picture:

Then, if the triangle is a right one, Pythagorean theorem must be fulfilled. This indicates that the sum of each of the squared legs must be equal to the hypotenuse squared, that is,

`12^2+16^2=20^2`

which gives

`144+256=400`

The left hand side is equal to 400, so we have that

`400=400`

so the sides belong to a righ triangle. So, Is the angle A a right angle? Answer: YES