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kcla1996

  • one year ago

Use the information in the diagram to determine the height of the tree to the nearest foot. A. 80 ft B. 264 ft C. 60 ft D. 72 ft

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  1. kcla1996
    • one year ago
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  2. e.mccormick
    • one year ago
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    OK. The double hash marks mean the tree to building distance is the same as the tree to observer. Now use rules of similar triangles and that one bit of information.

  3. kcla1996
    • one year ago
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    rules of similar triangles?

  4. e.mccormick
    • one year ago
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    Yes, if two triangles have the same shape, they are similar. Well, the tirangle from observer to building and observer to tree are similar. So the sides are rations of one another. Or, you can use trig to do the same thing. All depends on what you want to use, mathematically it is the same answer, but similar triangles is easiest in this case.

  5. e.mccormick
    • one year ago
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    Because that is true, what can you say about the ratio of the sides of the two triangles?

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  6. kcla1996
    • one year ago
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    they are different

  7. e.mccormick
    • one year ago
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    Well, the lengths of the sides are different, that is true. But there is a ratio between them. Let me see if I can find an easy reference on this principal that will make it clear.

  8. e.mccormick
    • one year ago
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    http://www.mathsisfun.com/geometry/triangles-similar.html That explains what similar triangles are. Now, because the observer to top of building to bottom of building triangle and the observer to top of tree to bottom of tree triangle are similar, you can use these rules here.

  9. e.mccormick
    • one year ago
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    Start by finding the total length from the observer to the building.

  10. kcla1996
    • one year ago
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    120 ft?

  11. e.mccormick
    • one year ago
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    That is the distance from the observer to the tree. Now, look at the edited picture where I circled those marks. If obserevr to tree and tree to building are the same, what is observer to building?

  12. kcla1996
    • one year ago
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    280 ft?

  13. e.mccormick
    • one year ago
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    120*2=? 280? Umm..

  14. e.mccormick
    • one year ago
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    You overshot there.... and I still make those mistakes in college, so it is not too surprising. Try again.

  15. kcla1996
    • one year ago
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    240?

  16. e.mccormick
    • one year ago
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    Yes. Now, do you know how to set up the ratio of the sides? You have the unknown height of the tree, the height of the building, the distance from the observer to the tree and the distance from the observer to the building. They need to be in a ratio and solved for the unknown one.

  17. kcla1996
    • one year ago
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    no i dont know

  18. e.mccormick
    • one year ago
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    OK. I am doing another editid pic. That will help explain it.

  19. e.mccormick
    • one year ago
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    Now, we now know that A=240. You are given the 120 and B=160. But C is the question. Tha is what we are dealing with. Now, do you know what a ratio is and how to solve them? If not, I can do a quick example.

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  20. e.mccormick
    • one year ago
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    Basic ratios: If 10 is to 30 as 7 is to x, what is x? This can be set up as a ratio one of two ways. \[\frac{ 10 }{ 30 } = \frac{ 7 }{ x } \,or\, \frac{ 30 }{ 10 } = \frac{ x }{ 7 } \]Either way you then solve for x. If 10 and 30 are two sides of a triangle and 7 and x are two sides of a similar triangle, this type of ratio can be used to solve for the unknown side of the second triangle. That is why ratios can solve this problem.

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