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math_crasher Group Title

Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale. Pls explain to me how to do this. Figure is below

  • one year ago
  • one year ago

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  1. math_crasher Group Title
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    • one year ago
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  2. cwrw238 Group Title
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    |dw:1346866520983:dw|

    • one year ago
  3. cwrw238 Group Title
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    the 2 triangles ACD and ABC are similar (same shape - corresponding angles are equal) the property of similar triangles is that corresponding sides are in the same ratio

    • one year ago
  4. math_crasher Group Title
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    awesome thanks

    • one year ago
  5. math_crasher Group Title
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    So the length of the altitude would be 147?

    • one year ago
  6. cwrw238 Group Title
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    no - i'm a bit confused myself now - not sure if we got enough info to do this

    • one year ago
  7. math_crasher Group Title
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    hmmm same here

    • one year ago
  8. math_crasher Group Title
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    I just multiplied 7 and 21 and figured it would be the geometric mean Xd

    • one year ago
  9. cwrw238 Group Title
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    no don't work like that take gig triangle the side opposite the right angle = 28 long right?

    • one year ago
  10. cwrw238 Group Title
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    *big triangle ABC

    • one year ago
  11. math_crasher Group Title
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    ok

    • one year ago
  12. cwrw238 Group Title
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    now look at small on ABD the side opposite right angle is AC AC is side corresponding to the one 28 long so the ratio is AC -- 28

    • one year ago
  13. math_crasher Group Title
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    Ah ok so you added 21 and 7 and that is equals to AC?

    • one year ago
  14. cwrw238 Group Title
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    no 21 and 7 = BC

    • one year ago
  15. cwrw238 Group Title
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    the way the triangles are its hard to explain |dw:1346867633370:dw|

    • one year ago
  16. math_crasher Group Title
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    That is hard T_T

    • one year ago
  17. cwrw238 Group Title
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    the 2 triangles are similar - the sides are different in length but the angles are same 3 in small trianglee corresponds to 6 in big one and 2 in small triangle corresponds to x in gig one righr?

    • one year ago
  18. math_crasher Group Title
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    right that means that x= 4 right?

    • one year ago
  19. cwrw238 Group Title
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    exactly 3/6 = 2/x so x = 4

    • one year ago
  20. math_crasher Group Title
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    But what am I trying to solve in the previous triangle?

    • one year ago
  21. cwrw238 Group Title
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    you need the height right? thats AD

    • one year ago
  22. math_crasher Group Title
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    I need the height of the altitude drawn to the hypotenuse

    • one year ago
  23. cwrw238 Group Title
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    yea - thas length of AD - BC is the hypotenuse of the big triangle ABC

    • one year ago
  24. math_crasher Group Title
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    ok

    • one year ago
  25. cwrw238 Group Title
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    but we have to find length of AC first because we only know the 2 values 7 and 21. - you'll see why later

    • one year ago
  26. math_crasher Group Title
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    oh ok so how do I solve for AC?

    • one year ago
  27. cwrw238 Group Title
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    by using similar triangle property we already got AC / 28 now look at the 2 triangles ABC and ACD the side CD (=7) in the small triangle is opposite the angle CAD right?

    • one year ago
  28. math_crasher Group Title
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    right

    • one year ago
  29. cwrw238 Group Title
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    |dw:1346868513347:dw|

    • one year ago
  30. cwrw238 Group Title
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    the 2 angles marked x are equal and the side opposite angle B in big triangle = AC so this means that the side correspond to CD in small triangle is corresponding to AC in big triangle

    • one year ago
  31. math_crasher Group Title
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    ok

    • one year ago
  32. cwrw238 Group Title
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    not easy to see this because the way the triangles are related ratio of these sides in small : big = 7 /AC and this equals AC / 28 which we got already

    • one year ago
  33. math_crasher Group Title
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    ah ok

    • one year ago
  34. cwrw238 Group Title
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    so AC 7 -- = -- 28 AC cross multiply AC^2 = 7*28 = 196

    • one year ago
  35. math_crasher Group Title
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    hmmm i see, ok

    • one year ago
  36. cwrw238 Group Title
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    so - the last step! apply pythagoras theorem to triangle ADC: AC^2 = 7^2 + AD^2 196 = 49 + ad^2 AD^2 = 196 - 49 = 147 AD = square root of 147

    • one year ago
  37. math_crasher Group Title
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    O.o ok

    • one year ago
  38. cwrw238 Group Title
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    yea - thats a tricky one - you get wingspan-eyed figuring out how 2 triangles are related

    • one year ago
  39. math_crasher Group Title
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    Ah ok i see

    • one year ago
  40. cwrw238 Group Title
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    -i think i'll take a break - lol!!

    • one year ago
  41. math_crasher Group Title
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    |dw:1346869580845:dw|

    • one year ago
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