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Math Help - Angular intersection.... i think trig is used but im well confused pls pls pls help

  1. #1
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    Red face Angular intersection.... i think trig is used but im well confused pls pls pls help

    Intersection.... how would u do this?
    the following clock wise angles were observed:
    at A from B to P the angle is 64d 42m 42s
    at B from A to P the angle is 296d 15m 31s

    the co-ordinates of A are 500E 500N
    the co-ordinates of B are 703.501E 240.809N
    Find the co-ordinates of P
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  2. #2
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    Quote Originally Posted by jane?? View Post
    Intersection.... how would u do this?
    the following clock wise angles were observed:
    at A from B to P the angle is 64d 42m 42s
    at B from A to P the angle is 296d 15m 31s

    the co-ordinates of A are 500E 500N
    the co-ordinates of B are 703.501E 240.809N
    Find the co-ordinates of P
    are these three points on a plane surface or a sphere?
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  3. #3
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    plane surface?? it doesnt say in the question but thats wat i would presume
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  4. #4
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    Quote Originally Posted by jane?? View Post
    Intersection.... how would u do this?
    the following clock wise angles were observed:
    at A from B to P the angle is 64d 42m 42s
    at B from A to P the angle is 296d 15m 31s

    the co-ordinates of A are 500E 500N
    the co-ordinates of B are 703.501E 240.809N
    Find the co-ordinates of P
    See the attached image.

    I have added two points:
    C is due north of point P &
    C is due west of point A
    D is due east of A
    Points D, A, & C all have north coordinate of 500.000
    ---
    The difference of the Northing coordinates from A to B:
    ( 240.809N - 500.000N ) = -259.191

    The difference of the Easting coordinates from A to B:
    ( 703.501E - 500.000E ) = +203.501

    The distance AB can be computed:
     \bar{AB} = \sqrt{ (-259.191)^2 + 203.501^2 } = 329.53396

    At this moment you should calculate the angle DAB
    since it will be needed later:

     \angle DAB = arctan \left ( \dfrac{259.191}{203.501} \right ) = 51d 51m 47s


    [NOTE: We know that DAB is a negative angle, but that attribute will be ignored]
    Angle CAP = 180d - ( 51d 51m 47s ) - ( 64d 42m 42s) = 63d 25m 31s <- NEED THIS!

    Angle APC = 90d - ( 63d 25m 31s ) = 26d 34m 29s <-- do not need this but there it is.

    ---
    You are given the interior angle BAP = 64d 42m 42s
    The interior angle at B is 360d - (296d 15m 31s) = 63d 44m 29m
    The third angle at P is: 180deg minus angles A & B
    ::
    180d - (64d 42m 42s) - (63d 44m 29m) = 51d 32m 49s

    Using the Rule of Sines (or The Law of Sines, or Sine Law)

     \dfrac{ AB }{ \sin (51d 32m 49s) } = \dfrac{ AP }{ \sin (63d 44m 29m)}

    which leads to

     \dfrac{ AB \times \sin (63d 44m 29m) }{ \sin (51d 32m 49s) } = AP

    We do not require the distance BP.

    ---
    The northing coordinates of P:
    North coord of A MINUS distance AP x sin(angle CAP)

     500.000 - AP \cdot \sin(63d 25m 31s)

    ---
    The easting coordinates of P:
    East coords of A MINUS distance AP x cos(angle CAP)

     500.000 - AP \cdot \sin(63d 25m 31s)

    ---
    Run this and determine the values.
    I will do the math parts later as a check.
    From the image it is clear that Point P is SOUTH & WEST of Point A.
    If you do not have the visual aid, it is imperative to be cognizant of the signs of the computed values.
    Attached Thumbnails Attached Thumbnails Angular intersection.... i think trig is used but im well confused pls pls pls help-mhf020001.jpg  
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  5. #5
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    thanks so much your a star i put up another question today can u have a look at it.... i wish i was good at maths lol
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