How Long is the Hypotenuse?Date: 07/12/99 at 11:10:34 From: Jon Mann Subject: Geometry Question In a right triangle, the lengths of the segments connecting the points of trisection of the hypotenuse to the vertex of the right angle are 7 and 9. How long is the hypotenuse of the triangle? Also, what are some generalizations that I can make about this sort of problem? Thank you. Date: 07/12/99 at 12:56:54 From: Doctor Peterson Subject: Re: Geometry Question Hi, Jon. If you draw segments from each trisection point parallel to the legs, you get something like this: + |\ a| \c | \ +---* | /|\ a| 9/| \c | / | \ +-/-+---* |/ | / |\ a|/ /7 | \c / / | | \ +---+---+---+ b b b You have a lot of congruent right triangles with sides a, b, and c, and two interesting ones with hypotenuse 7 and 9. Write the Pythagorean Theorem for each of these, and see what it tells you! Then see what happens if 7 and 9 are replaced by any other numbers. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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