Results 1 to 6 of 6

Math Help - trig problem

  1. #1
    Newbie
    Joined
    Apr 2013
    From
    australia
    Posts
    3

    trig problem

    Hi, i have just started a tafe course and have come across this problem. I have not taken trig in along time, any guidance would be appreciated.

    question.

    6. How do you find the length of the baseline AD when it is interrupted by an obstacle?

    trig problem-untitled2.jpg

    Length AB = 436.3m = x
    Length BC = ? = y, and
    Length CD = 542.8m = z.

    Problem: What is length BC?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,024
    Thanks
    741

    Re: trig problem

    Hey mcleod86.

    My advice would be to use the sine rule and write out all the relations you can for both the individual triangles and the large triangle as a whole.

    Are you aware of the sine rule?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2013
    From
    australia
    Posts
    3

    Re: trig problem

    Hi Chiro, thank you for the prompt reply,

    i know the sine rule
    a/sinA = b/sinB = c/sinC i tried 542.8/sin54 = x/sin137 but not sure... my answer did not look right.

    i have used interpolation to solve , does this look right ?

    y - 436 / 38 - 45 = 542 - 436 / 54 - 45

    y - 436 / -7 = 11.77

    y - 436 = 11.77(-7)

    y = -82.39 +436

    y = 353.61

    what do you think?
    thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,024
    Thanks
    741

    Re: trig problem

    Can you give me some reasoning behind your solution?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2013
    From
    australia
    Posts
    3

    Re: trig problem

    I thought If I find the ratio between the distance and degree of known values, i can find the unknown distance. yes? but now i think of it, it is not a linear relationship so this isn't correct, is it?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Mar 2013
    From
    Iowa, USA
    Posts
    37
    Thanks
    9

    Re: trig problem

    The first thing you have to do is work out all your angles, from what you have given.

    \angle AED = \alpha + \beta + \gamma = 45^{\circ}12'37'' + 38^{\circ}25'48'' + 54^{\circ}33'28'' = 138^{\circ}11'53''

    \angle EAD + \angle EDA = 180^{\circ} -138^{\circ}11'53'' = 41^{\circ}48'7''

    Let \angle EDA = \theta and let \angle EAD = 41^{\circ}48'7'' - \theta

    \angle ABE = 180^{\circ} - (45^{\circ}12'37'' + 41^{\circ}48'7'' - \theta) = 92^{\circ}59'16'' + \theta

    \angle DCE = 180^{\circ} - (54^{\circ}33'28'' + \theta) = 125^{\circ}26'32'' - \theta

    \angle ECB = 54^{\circ}33'28'' + \theta

    \angle EBC = 87^{\circ}00'44'' - \theta

    The law of sines is now applied to create the three equations needed to find the unknowns EC, EB and \theta

    \displaystyle\frac{\sin{54^{\circ}33'28''}}{542.8} = \displaystyle\frac{\sin{\theta}}{EC}

    \displaystyle\frac{\sin{45^{\circ}12'37''}}{436.3} = \displaystyle\frac{\sin(41^{\circ}48'7'' - \theta)}{EB}

    \displaystyle\frac{\sin(87^{\circ}00'44'' - \theta)}{EC} = \displaystyle\frac{\sin(54^{\circ}33'28'' + \theta)}{EB}

    Once you have solved for these unknowns then you can apply the law of sines to find BC, thus find AD


    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 20th 2012, 06:32 PM
  2. Trig word problem - solving a trig equation.
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: March 14th 2011, 08:07 AM
  3. Replies: 3
    Last Post: January 2nd 2011, 09:20 PM
  4. Trig problem
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: June 1st 2009, 06:56 PM
  5. trig problem
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: November 11th 2008, 05:06 PM

Search Tags


/mathhelpforum @mathhelpforum