Results 1 to 2 of 2

Math Help - Diagonal and Side of a Rhombus

  1. #1
    Mel
    Mel is offline
    Junior Member
    Joined
    Sep 2008
    Posts
    36

    Diagonal and Side of a Rhombus

    The shorter diagonal of a rhombus makes an angle of 78 degrees with a side of the rhombus. If the length of the shorter diagonal is 24, find to the nearest tenth the length of: (a) a side of the rhombus and (b) the longer diagonal.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by Mel View Post
    The shorter diagonal of a rhombus makes an angle of 78 degrees with a side of the rhombus. If the length of the shorter diagonal is 24, find to the nearest tenth the length of: (a) a side of the rhombus and (b) the longer diagonal.
    As a rhombus has all 4 sides of equal length each must be 24. From the angle of 78 it's supplementary angle must be 180-78 = 112 degrees.

    From there the cos rule can be used. Let c be the diagonal across the rhombus such that it meets the corners at the 78 degree angles:

    c^2 = a^2+b^2-2abcosC

    c^2 = 2a^2 - 2a^2cosC = 2a^2(1-cosC)

    a = 24 and C = 102
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving for side of square given diagonal
    Posted in the Geometry Forum
    Replies: 4
    Last Post: December 19th 2012, 05:28 PM
  2. Replies: 6
    Last Post: August 17th 2011, 04:42 AM
  3. rhombus diagonal
    Posted in the Geometry Forum
    Replies: 2
    Last Post: December 26th 2010, 05:03 AM
  4. Surds (length of a side of a rhombus)
    Posted in the Algebra Forum
    Replies: 5
    Last Post: June 6th 2010, 01:40 AM
  5. Replies: 0
    Last Post: October 15th 2008, 04:05 AM

Search Tags


/mathhelpforum @mathhelpforum