The Math Forum

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

Length of the Diagonals of a Parallelogram

Date: 05/22/2000 at 19:46:31
From: moose
Subject: Calculus

A parallelogram has a 70-degree angle and sides 6cm and 10cm long. How 
long are its diagonals?

Date: 05/23/2000 at 11:53:07
From: Doctor Douglas
Subject: Re: Calculus

Hi Moose,

This is more of a trigonometry/geometry problem than a calculus 
problem. First we draw a parallelogram:

       A --------------- P(x,y)
        /              /
     6 /              / 6
             10      B

Now, what is the length of say, the long diagonal? If we superimpose 
a Cartesian xy grid on this with the origin at the lower left, we then 
need to find the coordinates of the point P(x,y) at the upper right. 
We use trigonometry (see lower left angle, left side) to compute these 

    x = (bottom of triangle at left) + (upper edge)
      = (6 cos(70 deg)) + (10)

    y = (height of triangle at left)
      = (6 sin(70 deg))

So the long diagonal is sqrt(x^2 + y^2), by the Pythagorean theorem. 
See if you can use similar reasoning to obtain the coordinates of 
points A and B to find the length of the short diagonal.

- Doctor Douglas, The Math Forum   
Associated Topics:
High School Coordinate Plane Geometry
High School Geometry
High School Triangles and Other Polygons
High School Trigonometry

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.