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### Finding Angles

```
Date: 9/6/96 at 19:57:14
From: BARRY CALDWELL
Subject: Finding Angles of a Right Triangle

How do you compute the other two angles of a right triangle?  I
know the hypotenuse and the other two lengths, but how do I get the
other two angles?

Sincerely,
Barry Caldwell
```

```
Date: 9/6/96 at 20:16:0
From: Doctor Tom
Subject: Re: Finding Angles of a Right Triangle

Hi Barry,

To do this, you need trigonometry.

For example, suppose the hypotenuse is h and the two sides are
a and b.

To find the angle between a and the hypotenuse (I'll call it x),
notice that the tangent of x = b/a.  Work out b/a (it'll just be
a number), and then find what angle has this number as its
tangent.

This is done by taking the arc tangent.  On your calculator, it'll
be marked as "atan", or "arctan", or "tan^(-1)", or something
like that.

Similarly for the other angle.

Don't worry about not using the value of h.  It, after all, depends
on a and b, and the arctangent function takes that into account.

You can do a similar thing (using the h) with the arcsin or
arccosine functions.  I just happened to decide to use the
arctangent because I happen to know something about the stability
of numerical calculations involving it, but with a "perfect"
calculator, it doesn't matter.

-Doctor Tom,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Trigonometry

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