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Law of Sines Word Problem (Photo Included)

  1. Nov 20, 2009 #1
    1. The problem statement, all variables and given/known data

    The leaning tower of Pisa was originally perpendicular to the ground and 179ft tall. Because of sinking into the earth, it now leans at a certain angle 'theta' from the perpendicular, as shown in the figure. When the top of the tower is viewed from a point 150ft from teh center of its base, the angle of elevation is 53 degrees.

    a) Approximate the angle theta.

    b) Approximate the distance d that the center of the top of the tower has moved from the perpendicular.

    Here is the photo. I apologize for the blurry photo. If needed I'll try to get my real camera and take a better one.
    4120399249_a3f62a33dc.jpg

    2. Relevant equations

    Law of Sines. Maybe one can solve this by other means, but it is implied I can do this with Law of Sines alone.

    3. The attempt at a solution

    I know the height of the tower is the the length of one side of the right triangle (the straight line on the tower in the photo). I'm not sure if that is also true for the line the represents how the tower leans. I'm not sure where to start with this as a result. I think I need a nudge in the right direction.

    Thanks!
     
    Last edited: Nov 20, 2009
  2. jcsd
  3. Nov 20, 2009 #2
    you know that:

    [tex]\frac{sin(53)}{H_a}[/tex] - with [tex]H_a[/tex] being the height after

    is equal to what?
     
  4. Nov 20, 2009 #3
    That would equal to sin c\150 feet. That is, if sin c is the angle at the top for the triangle involving Ha.

    Am I supposed to know how to get that angle..or am I really off track?
     
  5. Nov 21, 2009 #4
    yes.
     
  6. Nov 21, 2009 #5
    OK, I slept on it and worked on it a bit more this morning. I think the angle that is opposite to the ground is 37 degrees. Therefore:

    sin 53\Ha=sin 37\150

    I found this angle by finding all angles of the right triangle and then creating two more right triangles between the perpendicular and Ha.
     
  7. Nov 21, 2009 #6
    But 37 is no longer the third angle after the tower has leaned no?
     
  8. Nov 21, 2009 #7
    I thought that was odd. I just don't know how to find this angle. After leaning, should it be larger than 37 degrees?
     
  9. Nov 21, 2009 #8
    OK I think I have a correct answer. The angle theta is 5 degrees and the distance d is about 15.7 feet. I let the length of the perpendicular and the leaning part be equal to 179 feet. I don't know if that's what the diagram implied though.
     
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