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math_crasher

  • 2 years ago

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

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  1. math_crasher
    • 2 years ago
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  2. cwrw238
    • 2 years ago
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    |dw:1346866520983:dw|

  3. cwrw238
    • 2 years ago
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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

  4. math_crasher
    • 2 years ago
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    awesome thanks

  5. math_crasher
    • 2 years ago
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    So the length of the altitude would be 147?

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

  7. math_crasher
    • 2 years ago
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    hmmm same here

  8. math_crasher
    • 2 years ago
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    I just multiplied 7 and 21 and figured it would be the geometric mean Xd

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

  10. cwrw238
    • 2 years ago
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    *big triangle ABC

  11. math_crasher
    • 2 years ago
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    ok

  12. cwrw238
    • 2 years ago
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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

  13. math_crasher
    • 2 years ago
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    Ah ok so you added 21 and 7 and that is equals to AC?

  14. cwrw238
    • 2 years ago
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    no 21 and 7 = BC

  15. cwrw238
    • 2 years ago
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    the way the triangles are its hard to explain |dw:1346867633370:dw|

  16. math_crasher
    • 2 years ago
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    That is hard T_T

  17. cwrw238
    • 2 years ago
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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?

  18. math_crasher
    • 2 years ago
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    right that means that x= 4 right?

  19. cwrw238
    • 2 years ago
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    exactly 3/6 = 2/x so x = 4

  20. math_crasher
    • 2 years ago
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    But what am I trying to solve in the previous triangle?

  21. cwrw238
    • 2 years ago
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    you need the height right? thats AD

  22. math_crasher
    • 2 years ago
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    I need the height of the altitude drawn to the hypotenuse

  23. cwrw238
    • 2 years ago
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    yea - thas length of AD - BC is the hypotenuse of the big triangle ABC

  24. math_crasher
    • 2 years ago
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    ok

  25. cwrw238
    • 2 years ago
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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

  26. math_crasher
    • 2 years ago
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    oh ok so how do I solve for AC?

  27. cwrw238
    • 2 years ago
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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?

  28. math_crasher
    • 2 years ago
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    right

  29. cwrw238
    • 2 years ago
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    |dw:1346868513347:dw|

  30. cwrw238
    • 2 years ago
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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

  31. math_crasher
    • 2 years ago
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    ok

  32. cwrw238
    • 2 years ago
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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

  33. math_crasher
    • 2 years ago
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    ah ok

  34. cwrw238
    • 2 years ago
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    so AC 7 -- = -- 28 AC cross multiply AC^2 = 7*28 = 196

  35. math_crasher
    • 2 years ago
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    hmmm i see, ok

  36. cwrw238
    • 2 years ago
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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

  37. math_crasher
    • 2 years ago
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    O.o ok

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

  39. math_crasher
    • 2 years ago
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    Ah ok i see

  40. cwrw238
    • 2 years ago
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    -i think i'll take a break - lol!!

  41. math_crasher
    • 2 years ago
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    |dw:1346869580845:dw|

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