Results 1 to 7 of 7

Math Help - Triangle question

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    12

    Triangle question

    Hi!

    How can I count the surface area of an isosceles triangle + lengths of all sides + count the angles ?

    I only know the height of the isosceles triangle and the base angle too.


    Thanks for your help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by WendyM View Post
    Hi!

    How can I count the surface area of an isosceles triangle + lengths of all sides + count the angles ?

    I only know the height of the isosceles triangle and the base angle too.


    Thanks for your help!
    Let b denote the length of the base, l the length of the two equal legs, h the height and \alpha the angle at the base.

    You can split the isosceles triangle into two congruent right triangles. Then you have:

    \tan(\alpha) = \dfrac{h}{\frac12 b} Solve for b.

    \sin(\alpha) = \dfrac hl Solve for l

    The area is

    a=\dfrac12 \cdot b \cdot h

    Plug in the values you now know.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    12
    Thanks. But I only know the angle of the base so how can i get the solve for b by multiplying * b if I don't know the length of the base just the base angle.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Dec 2008
    Posts
    152
    <br />
tan \phi = \frac {h}{\frac{1}{2}b} \Rightarrow \frac {1}{2}b = \frac {h}{tan \phi} \Rightarrow b = \frac {2h}{tan \phi}<br />

    You said you knew the angle and the height.. If you know these 2 you can calculate the base b from the equation posted by earthboth. (I just turned it a bit incase you were confused by it)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Arrow

    Quote Originally Posted by WendyM View Post
    Thanks. But I only know the angle of the base so how can i get the solve for b by multiplying * b if I don't know the length of the base just the base angle.
    Read earboth's post again. He tells you how to find b\text.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Feb 2009
    Posts
    12
    I just don't get it

    Please don't spoil my task, but give me an example if the height of the isosceles triangle was: 200m, 250m, 300m... (You can choose one)
    and the base angle was: 15 degrees, 20, 25...(You can choose one)

    How will I find out what is the surface area of it?

    Lengths of all sides of it?

    Count the angles?

    Please give an example with numbers?
    I'd really appreciate it!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by WendyM View Post
    ... give me an example if the height of the isosceles triangle was: 200m, 250m, 300m... (You can choose one)
    and the base angle was: 15 degrees, 20, 25...(You can choose one)

    How will I find out what is the surface area of it?

    Lengths of all sides of it?

    Count the angles?

    Please give an example with numbers?
    I'd really appreciate it!
    1. Why didn't you post a question using numbers?

    2. I've attached a sketch of an isosceles triangle. H denotes the height and b the base of the triangle.

    3. Example: |\alpha| = 42^\circ , |h| = 12\ cm (I use these values so you have the opportunity to control the results by a (more or less) exact construction)

    4. Results:
    \tan(42^\circ)=\dfrac{12\ cm}{\frac12 b}~\implies~ b = 2 \cdot \dfrac{12\ cm}{\tan(42^\circ)} \approx 21.61\ cm

    \dfrac hl=\sin(42^\circ)~\implies~l=\dfrac{12\ cm}{\sin(42^\circ)}\approx 17.93\ cm
    area:

    a = \frac12 \cdot b \cdot h~\implies~a=\frac12 \cdot 21.61\ cm \cdot 12\ cm \approx 129.66\ cm^2
    Attached Thumbnails Attached Thumbnails Triangle question-gl_schenklg_3eck.png  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Triangle question
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 2nd 2010, 12:37 AM
  2. Triangle dz/dt question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 8th 2010, 12:29 PM
  3. Triangle question
    Posted in the Geometry Forum
    Replies: 5
    Last Post: June 27th 2009, 01:50 AM
  4. triangle question
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 18th 2008, 11:16 AM
  5. A triangle question
    Posted in the Algebra Forum
    Replies: 3
    Last Post: August 25th 2005, 01:24 AM

Search Tags


/mathhelpforum @mathhelpforum