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Finding height using the direction cosines

  1. Oct 4, 2009 #1
    Sorry for the re-post

    1. The problem statement, all variables and given/known data

    http://books.google.ca/books?id=nYR...g direction cosines to measure height&f=false

    The obove link has a coopy of the question as it is hard to describe.

    If you find the link is too hard to read here is the data
    Direction cosines:

    of Rap(from point a to top of mountain):
    cos theta x= .5179
    cos theta y= .6906
    cos theta z= .5048

    of Rbp(from point b to top of mountain):
    cos theta x=-.3743
    cos theta y=.7486
    cos theta z=.5472

    b and a are 10000m apart. Find how high point p is.
    It is on page 57 #2.82 (The mount everest question)

    2. Relevant equations



    3. The attempt at a solution
    I attemted the question in a number of ways but can't seem to come to an answer. I tried Looking at it as two right angled triangles and using trig. Im not really sure what i can do with the direction cosines either.
     
  2. jcsd
  3. Oct 5, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    Draw a perpendicular PO on the base of the mountain. Let PD, PE and PF on x, y and z axis passing through A.
    AD = AP*cos(α)
    AE = AP*cos(β)
    [cos(α) = 0.5179, cos(β) = 0.6906]
    Now tan(OAD) = AE/AD. Find angle OAD. Similarly find angle OBD. from these two angles find the third angle AOB. Using sine rule in the triangle AOB, find Ao and BO.
    cos(γ) = 0.5048 is given. From that find tan(γ) which is equal to PO/AO. AO is known. Find PO.
     
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