The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Angle, Side Length of a Triangle

Date: 9/4/96 at 17:19:5
From: Robert Inman
Subject: Angle, Side Length of a Triangle

Hi Dr. Math,     

What is the relation between the angles of a triangle and the length 
of its sides? For example, if I know that a triangle has a 90 degree 
angle, I know the length of one leg, and the angle between that leg 
and the hypotenuse, how do I determine the length of the other leg? 

Date: 9/4/96 at 18:53:10
From: Doctor Tom
Subject: Re: Angle, Side Length of a Triangle

Hi Robert,

One simple relation is that the bigger the angle, the bigger the side 
opposite it.

There's an exact relation called the "law of sines".  Assume that your 
triangle has sides of length A, B, and C.  Assume also that the angle 
opposite side A is a, opposite B is b, and opposite C is c.  The law 
of sines states:

  sin a   sin b   sin c
  ----- = ----- = -----
    A       B       C

Unfortunately, it uses trigonometry.  You can look up the values of
the sines of angles in tables, or using some calculators.

The "law of cosines" is also sometimes valuable.  It states that:

  C^2 = A^2 + B^2 - 2ABcos c

with the same labels as above.  "cos" is the cosine function, and
I use "^" to indicate an exponent: "C^2" is "C squared".

"Trigonometry" comes from the Greek: "trig" - triangle, and
"metry" - measurement.  That's exactly what you're trying to
do, right?

-Doctor Tom,  The Math Forum
 Check out our web site!   
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
High School Triangles and Other Polygons
High School Trigonometry
Middle School Geometry
Middle School Triangles and Other Polygons
Middle School Two-Dimensional Geometry

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.