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rebeccaskell94

  • 2 years ago

In △PQR, what is the length of line segment QR? http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0404_02/image0064e2eda71.gif 28 28radical 2 56radical 3 56radical 2 *I think the answer is A?*

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  1. phi
    • 2 years ago
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    this is a "special right triangle" 45-45-90 The idea is to remember that the hypotenuse (longest side, opposite the 90 deg angle) is sqrt(2) times bigger than either leg (which are equal) h = a*sqrt(2) or (divide by sqrt(2) ) a= h/sqrt(2)

  2. phi
    • 2 years ago
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    or (because people do not sqrt(2) in the denominator) a= sqrt(2)*h/(sqrt(2)*sqrt(2)) (multiply top and bottom by sqrt(2)) you do this to get rid of the sqrt(2) in the bottom a= sqrt(2)*h/2

  3. rebeccaskell94
    • 2 years ago
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    Whoa. That was a lot.

  4. phi
    • 2 years ago
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    too much to get the answer?

  5. rebeccaskell94
    • 2 years ago
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    I'm not sure. I'm looking at it like @ . @

  6. phi
    • 2 years ago
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    the side is h/sqrt(2)= 56/sqrt(2) but none of your answers are in that form. so we have to "rationalize" to get an answer that matches.

  7. rebeccaskell94
    • 2 years ago
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    @Parthkohli this one :D If you are given a leg of a 45-45-90 triangle, you just put 2√ in front of it to get the hypotenuse ^_^ • If the leg is 8, then the hypotenuse is 82√ • If the leg is 1281283283283249483483, then the hypotenuse is 12812832832832494834832√

  8. ParthKohli
    • 2 years ago
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    The short-cut that I gave you doesn't work here too much, FYI. I just told you in simple words to remove/put sqrt2. What that short-cut actually says is that you have to multiply sqrt2 to get the hypotenuse and divide sqrt2 from the hypotenuse to get the leg.

  9. kaiz122
    • 2 years ago
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    can we just use trigo. here? \[\cos \theta =\frac{adjacent}{hyp}\]

  10. ParthKohli
    • 2 years ago
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    So, you divide \(\sqrt2\) from the hypotenuse to get the leg.

  11. kaiz122
    • 2 years ago
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    adjacent=(cos 45)*56

  12. ParthKohli
    • 2 years ago
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    Or, the Pythagorean. \( \color{Black}{\Rightarrow a^2 + a^2 = 56^2 }\) \( \color{Black}{\Rightarrow 2a^2 = 3136}\)

  13. ParthKohli
    • 2 years ago
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    If you ever get confused with that short-cut, just come back to Pythagorean ;)

  14. rebeccaskell94
    • 2 years ago
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    Ah! okay um wait...that just goes back to 28?

  15. ParthKohli
    • 2 years ago
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    \( \color{Black}{\Rightarrow a^2 = 1568}\) You find \(\sqrt{1568}\).

  16. ParthKohli
    • 2 years ago
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    (In radical form).

  17. rebeccaskell94
    • 2 years ago
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    Okay √1568 = 39.5 and 28√2 = 39.5 as well :D

  18. ParthKohli
    • 2 years ago
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    Yep :)

  19. rebeccaskell94
    • 2 years ago
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    Yay :D Thanks

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