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Math Help - Triangle Equation Question

  1. #1
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    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

    Please help
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  2. #2
    Member pflo's Avatar
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    Quote Originally Posted by Sam1111 View Post
    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

    Please help
    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.
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