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Finding Angles

Date: 9/6/96 at 19:57:14
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?
   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

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.

So the answer is arctan(b/a).

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
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Associated Topics:
High School Trigonometry

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