Question

3. 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. (Be sure to show all work and/or reasoning.) PLEASE USE RATIOS NOT COSINE AND PLEASE PLEASE PLEEEEEAAAAAAAAAASE SHOW YOUR REASONING AND WORK!
Triangle ABC:
AB = 63, AC = 16, CB (hypotenuse thing) = 65

Answer 1

Sin < C =  63/65    so m < C =  75.75 degrees

and tan B = 16/63  so m <B =  14.25 degrees

m < C + m<B = 75.75 + 14.25  = 90 degrees

Therefore m < A   = 180-90 = 90


therefore the triangle is right-angled.