# Thread: Triangle Equation Question

1. ## Triangle Equation Question

Hey

I have this right angle triangle with 'a' as the adjacent, '8' as the opposite and 'h' as the hypotenuse.

Why do a and h satisfy the equation a*h=8^2

2. Originally Posted by Sam1111
Hey

I have this right angle triangle with 'a' as the adjacent, '8' as the opposite and 'h' as the hypotenuse.

Why do a and h satisfy the equation a*h=8^2

They don't.

If it is a right triangle, then you know $h^2 =a ^2 + 8^2$. You could solve your original equation for a, then plug it into the pythagorean theorem and solve for h. This would mean h MUST be approximately 10.176. Plugging that back into your original equation, you would find a MUST be approximately 6.289.

On the other hand, if you sketch a quick picture of what you are given about your triangle, then you can see that there are no such limitations on a and h. As leg a gets longer, hypotenuse h gets longer too. In fact, ANY values for a and h that satisfy the pythagorean theorem would work. Thinking of it another way, none of the triangle congruence theora would be satisfied if I had another triangle with the characteristics you describe. Hence, my triangle might not be congruent and might NOT have the lengths calculated above.