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Math Help - Geometry Triangles

  1. #1
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    Geometry Triangles

    I was working on a problem. I know that I am supposed to solve for the unknown. I just don't know what exactly the unknown is.

    Here is the problem-

    I can look out my window and see the top of a tower. On the map, I see that it is 2 miles away. I read somewhere that the tower is 500 feet tall. As I look at the tower, I see that the top leaves of a tree sometimes get in the way of the top of the tower. The tree is 50 yards from where I sit. How tall is the tree?

    How do I put this problem into an equation and what is the equation?

    Thanks for all potential help.
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  2. #2
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    Hello,
    Quote Originally Posted by KevinVM20 View Post
    I was working on a problem. I know that I am supposed to solve for the unknown. I just don't know what exactly the unknown is.

    Here is the problem-

    I can look out my window and see the top of a tower. On the map, I see that it is 2 miles away. I read somewhere that the tower is 500 feet tall. As I look at the tower, I see that the top leaves of a tree sometimes get in the way of the top of the tower. The tree is 50 yards from where I sit. How tall is the tree?

    How do I put this problem into an equation and what is the equation?

    Thanks for all potential help.
    Do you know how to use the Intercept theorem ?
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  4. #4
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    Hello, KevinVM20!

    To answer your first question:
    . . the unknown is obviously the height of the tree.


    I can look out my window and see the top of a tower.
    On the map, I see that it is 2 miles away.
    I read somewhere that the tower is 500 feet tall.
    As I look at the tower, I see that the top leaves of a tree
    sometimes get in the way of the top of the tower. **
    The tree is 50 yards from where I sit.
    How tall is the tree?
    ** I assume this means that the top of tree lines up
    . . with the line-of-sight to the top of the tower.

    We further assume that your eye and the base of the tower are at the same height.

    Let h = height of the tree (in feet).
    Change all units to feet.
    Code:
                                  *
                              *   |
                          *       |
                      *           | 500
                  *   |h          |
              *       |           |
          * - - - - - * - - - - - *
          : -  150  - :
          : - - - 10,560  - - - - :

    From the two similar right triangles, we have: . \frac{h}{150} \:=\:\frac{500}{10,560}

    Therefore: . h \;=\;\frac{75,000}{10,560} \;=\;\frac{625}{88} \;\approx\;7.1\text{ feet}


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  5. #5
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    Thank you very much Soroban! I now have a better understanding.



    Quote Originally Posted by Soroban View Post
    Hello, KevinVM20!

    To answer your first question:
    . . the unknown is obviously the height of the tree.


    ** I assume this means that the top of tree lines up
    . . with the line-of-sight to the top of the tower.

    We further assume that your eye and the base of the tower are at the same height.

    Let h = height of the tree (in feet).
    Change all units to feet.
    Code:
                                  *
                              *   |
                          *       |
                      *           | 500
                  *   |h          |
              *       |           |
          * - - - - - * - - - - - *
          : -  150  - :
          : - - - 10,560  - - - - :

    From the two similar right triangles, we have: . \frac{h}{150} \:=\:\frac{500}{10,560}

    Therefore: . h \;=\;\frac{75,000}{10,560} \;=\;\frac{625}{88} \;\approx\;7.1\text{ feet}


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