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Geometry HELP PLEASE!

  1. Jul 21, 2011 #1
    Geometry HELP!!!! PLEASE!

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

    A tree is leaning 14 degrees from the vertical. The tree casts a 40 foot shadow on the flat ground. The line from the trees shadow to the top of tree creates a 60 degree angle above the horizontal. I need to find the lenght of the tree.

    2. Relevant equations



    3. The attempt at a solution
    I tried everything, i know of but im stuck. I tried using trig but that only gave the lenghts for the outside of the right triangle the tree divides. I need help desperately!!
     

    Attached Files:

    Last edited: Jul 21, 2011
  2. jcsd
  3. Jul 21, 2011 #2
    Re: Geometry HELP!!!! PLEASE!

    The question seems to be missing....you might also want to draw a diagram.
     
  4. Jul 21, 2011 #3
    Re: Geometry HELP!!!! PLEASE!

    Ok , Im sorry I didnt realize , that i was the only one with the picture in front of me :) Here you go.
     
  5. Jul 21, 2011 #4
    Re: Geometry HELP!!!! PLEASE!

    Do you know the sine rule?
     
  6. Jul 21, 2011 #5
    Re: Geometry HELP!!!! PLEASE!

    No, can you explain to to me?
     
  7. Jul 21, 2011 #6
  8. Jul 21, 2011 #7
    Re: Geometry HELP!!!! PLEASE!

    So to use the sine rule i dont need a right triangle?
     
  9. Jul 21, 2011 #8
    Re: Geometry HELP!!!! PLEASE!

    No, it can be applied to any triangle.
     
  10. Jul 21, 2011 #9
    Re: Geometry HELP!!!! PLEASE!

    Im sorry that above question is rather stupid. However based on that explanation from the link, I dont understand this part :

    That gives c=2sin(105o)/sin(30o)
    which is 4sin(105o).

    We can write sin(105o) as sin(150o-45o) then use the sin(A-B) rule to write this as
    sin(150o)cos(45o)-cos(150o)sin(45o)
    Im confused as to why we can write the above statement. Does it change the answer?
     
  11. Jul 21, 2011 #10
    Re: Geometry HELP!!!! PLEASE!

    The two answers you get are equivalent, since you applied the identity to sin(105)

    4sin(105o)=4( sin(150o)cos(45o)-cos(150o)sin(45o) )
     
  12. Jul 21, 2011 #11
    Re: Geometry HELP!!!! PLEASE!

    Ok Great! then according to my calculations the lenght of the tree is 49.8677 ft
     
  13. Jul 29, 2011 #12

    PeterO

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    Homework Helper

    Re: Geometry HELP!!!! PLEASE!

    If when you drew your diagram, you made the 60 degree angle something like 60 degrees, rather than only 30 - 35 degrees, you would get some feedback from the diagram. [Notice that the angle you have marked as 44 appears BIGGER than the angle you have marked 60; it is even bigger than the angle you have marked 136]

    Since the shadow is 40' long, if your calculation is correct the "tree" should appear longer. [in a perfect scale diagram, the tree would be close to 125% the length of the shadow]

    If you are going to draw a diagram, at least make it close to the real thing - just so you get a pictorial indication that your calculation is correct.

    Peter
     
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