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,
Chris

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
  http://mathforum.org/dr.math/