Results 1 to 10 of 10

Thread: triangles and trig and all that

  1. #1

    Thread Starter
    PowerPoster
    Join Date
    Jul 1999
    Posts
    5,923

    triangles and trig and all that

    I need to get the length of the red line (height of the triangle), and the length of the black and the green line too

    The green and black lines combined are 500

    Also, the entire triangle won't necessary be a right-angled one

    Thanks to anyone who can help, I'm brain dead at the moment

    Attached Images Attached Images  

  2. #2
    Member Aerials's Avatar
    Join Date
    Jul 2002
    Location
    Chile
    Posts
    50
    posted it in galah but its 240

  3. #3

    Thread Starter
    PowerPoster
    Join Date
    Jul 1999
    Posts
    5,923
    that's good thanks but how did you get that...i need to be able to do it for any length of sides

  4. #4
    Fanatic Member bugzpodder's Avatar
    Join Date
    Jun 2002
    Location
    Ontario, Canada
    Posts
    787
    write the black line as x, so the green line is (500-x). let the red line be k. set up two pythagorus equations. solve for x. then solve for k.
    Massey RuleZ! ^-^__Cheers!__^-^ Massey RuleZ!


    Did you know that...
    The probability that a random rational number has an even denominator is 1/3 (Salamin and Gosper 1972)? This result is independently verified by me (2002)!

  5. #5
    Fanatic Member sql_lall's Avatar
    Join Date
    Jul 2002
    Location
    Up Above (i.e. AUS)
    Posts
    571

    right angled

    Another possible way using areas:
    1) Work out the angle opposite the side 300 (use cosine rule)
    2) Work out the area using this angle and the sine rule
    3) Divid the area by 2, then by 500, and you get the height

    i.e. cos (A) = (400^2 + 500^2 - 300^2)/(2*400*500)
    => work out A
    => know sin(A) = (1- cos(A)^2) ^ 1/2
    => know area = 1/2 * 400 * 500 * sin(A)
    => know height = area/(2*500)
    => work out green line using cosine rule in 400-red line-green line triangle
    => work out black line = 500-green line
    sql_lall

  6. #6
    Addicted Member
    Join Date
    Aug 2002
    Location
    London UK
    Posts
    255
    The entire triangle must be right angled, because it obeys pythagoras theorem.

    Try two simultaneous equations with the sine rule (calling the red line R):

    Call black line X and red line R, angles in degrees for ease of use:

    sin60 / R = sin30 / X
    X/2 = R(Root3/2)
    X = R(Root3)

    sin30 / R = sin60 / (500 - X)

    Sticking in for X, that gets you:
    1 / 2R = (Root3/2) / (500 - R(Root3))

    So R = 250 / Root3 = 144.33756729740644112728719512549...

    Now that's assuming those angles are what I educatedly guessed them to be. I mean it all looks nice and neat that way.
    Not at all related to sheep...

  7. #7
    Addicted Member
    Join Date
    Aug 2002
    Location
    London UK
    Posts
    255
    And for my next amazing feat of genius, I will disappear from these forums for an entire week because I'm going skiing in France! Cyas!
    Not at all related to sheep...

  8. #8
    Addicted Member
    Join Date
    Aug 2002
    Location
    Windsor, Ontario's City of Pollution
    Posts
    165
    Use Heron's Formula; it has never failed since I used it to solve the first difficult geometry problem that I could do.
    Merry Math Making!

  9. #9
    Fanatic Member bugzpodder's Avatar
    Join Date
    Jun 2002
    Location
    Ontario, Canada
    Posts
    787
    with Assbandit noticing that A+B=90, and you know the side lengths, use the law of tangents!
    Massey RuleZ! ^-^__Cheers!__^-^ Massey RuleZ!


    Did you know that...
    The probability that a random rational number has an even denominator is 1/3 (Salamin and Gosper 1972)? This result is independently verified by me (2002)!

  10. #10
    Fanatic Member sql_lall's Avatar
    Join Date
    Jul 2002
    Location
    Up Above (i.e. AUS)
    Posts
    571

    Talking Fastest

    The fastese way to do it on that diagram is, knowing that it is a right-angled triangle, is say that redline*500 = 300*400 (= 2*area)
    => redline = 300*400/500
    = 3*400/5 = 3*80 = 240
    Green/Red = Red/Black
    => 240^2 = Green(500-Green) = 500 Green - Green^2
    => green^2 - 500 green + 240^2 = 0
    (green - 180)(green-320) = 0
    => green = 320, black = 180 (green>black)
    sql_lall

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  



Click Here to Expand Forum to Full Width