Question

Medal
One method you can use to determine whether a triangle is a right triangle, given three side lengths, is to apply the Converse of the Pythagorean Theorem. Alternately, you can use trigonometric ratios. Show that the triangle in the diagram is a right triangle by using trigonometric ratios.

Answer 1

You can solve this in a number of ways by using trigonometric ratios, for example, take any one angle, except the one that is the right angle itself, and you know that by looking at the longest side - the angle opposite to the longest side is the right angle, and find the value of sine, cosine and tangent of that angle by using the SOHCAHTOA method. Then plug in the three values you got above into the quotient relation between these three trigonometric ratios: tan(x) = sin(x)/cos(x).