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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.

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/
```
Associated Topics:
High School Triangles and Other Polygons
Middle School Triangles and Other Polygons

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