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Three Facts Necessary to Find a Triangle

Date: 09/13/2002 at 10:50:02
From: Chris Engle
Subject: Right Triangles, Advanced Pythagorean Theorem

I was wondering if there were any formulas where one could solve for a 
right triangle given only the length of one leg and no angles except 
for the known 90-degree angle. 

For example, a right triangle with one leg equaling 15 units the right 
angle 0 degrees.

  ? /  |
   /   |-15 units
  /   _|
 /?  | |-90 degree angle

I would like o know if there are any known formulas for solving for 
the other leg and the hypotenuse without using the 90-degree angle, 
i.e. without using sin, cos, or tan.

Thanks in advance. Sincerely,

Date: 09/13/2002 at 12:02:14
From: Doctor Peterson
Subject: Re: Right Triangles, Advanced Pythagorean Theorem

Hi, Chris.

There is not enough information here. In general, you need three facts 
about a triangle in order to determine the triangle (that is, to be 
able to know just what triangle it is); but you know only two.

For example, this will fit the known facts about your triangle just 
as well as the one you drew:

          / ?|
      ? /    |
      /      |-15 units
    /       _|
  /?       | |-90 degree angle
But all the "?"s are different in this triangle. So there is no way 
to find their values.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum 
Associated Topics:
High School Triangles and Other Polygons
Middle School Triangles and Other Polygons

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