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In a right triangle , if the hypotenuse is four times as long as the perpendicular from the opposite vertex , one of the acute angles is?

  • one year ago
  • one year ago

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  1. jhonyy9
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    can you draw it please ?

    • one year ago
  2. Yahoo!
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    pic us not given..

    • one year ago
  3. jhonyy9
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    indifferent just for what is your oppinion from this pic

    • one year ago
  4. heena
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    |dw:1339328315880:dw| i gues its like dis

    • one year ago
  5. apoorvk
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    |dw:1339328315376:dw|

    • one year ago
  6. heena
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    my ans is theta=cos-1(1/4)

    • one year ago
  7. apoorvk
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    @heena - wrong answer. Read the question again.

    • one year ago
  8. heena
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    i did and i dont find any prob as its saying hypotenuse is four times as long as the perpendicular means we cas asume perpendicular as x and hypotenuse as 4x

    • one year ago
  9. AndrewNJ
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    |dw:1339328062826:dw| i draw the pic u can find ab=4x^2 ---1 and a^2+b^2=16x^2 ----2 and use ab to represent x^2 at equation 2 we can have a^2+b^2=4ab devide ab two sides, that is a/b+b/a=4 we can let a/b=tanx (x could be the angle of one of two unknown angles) so tanx+1/(tanx)=4 let tanx=n so n+1/n=4, we can rewrite it as n^2-4n+1=0 and \[n=2\pm \sqrt{3}\] \[\tan x= 2\pm \sqrt{3}\] and u can work out the value of x that is the angle

    • one year ago
  10. Yahoo!
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    The options 60 45 30 15

    • one year ago
  11. FoolForMath
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    The correct answer is \(15^\circ \)

    • one year ago
  12. Yahoo!
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    @FoolForMath u r correct how????? PLzz show it!

    • one year ago
  13. apoorvk
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    lol sorry!! \[tan(15^o) = 2 - \sqrt3\] and the other angle will automatically be 90-15 = 75 degrees.

    • one year ago
  14. FoolForMath
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    Well, I can think of a radical free beautiful solution :)

    • one year ago
  15. Yahoo!
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    i did nt understand the method used!

    • one year ago
  16. apoorvk
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    Don't just think, share it with us. @FoolForMath -_-

    • one year ago
  17. Yahoo!
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    @AndrewNJ can u xplain it!

    • one year ago
  18. AndrewNJ
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    in my answer, the equation 1 ab=4x^2 for area of the triangle equals 0.5ab or 0.5*4x*x

    • one year ago
  19. Yahoo!
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    No Idea!

    • one year ago
  20. AndrewNJ
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    the equation 2, a^2+b^2=4ab means Pythagorean Theorem

    • one year ago
  21. Yahoo!
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    Side a is hypot

    • one year ago
  22. AndrewNJ
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    ok, dont be serious about a and b which is longer, it doesnt matter a is perpendicular to b so 0.5ab is the area of this triangle

    • one year ago
  23. AndrewNJ
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    and half of hypotenuse times its attitude is also the area of triangle

    • one year ago
  24. AndrewNJ
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    so these two part, 0.5ab and 0.5*4x*x can be equal

    • one year ago
  25. AndrewNJ
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    this is the first equation

    • one year ago
  26. AndrewNJ
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    the second is accroading to Pythagorean Theorem can u got it?

    • one year ago
  27. AndrewNJ
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    by the way hypotenuse is the longest side in a right triangle

    • one year ago
  28. FoolForMath
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    |dw:1339329313013:dw| \[\frac{AM}{MB }= \tan \alpha \] \[ \frac{AM}{MC}=\cot \alpha \] Thus,\[MB+MC =AM(\cot \alpha +\tan \alpha) \] \[\implies BC = 4AM=2AM \frac{1}{ \sin 2 \alpha}\] \[\implies \sin 2\alpha =\frac 12 \implies \alpha = 15^\circ \]

    • one year ago
  29. Yahoo!
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    @AndrewNJ i have a doubt in ur 1 st eq a^2=4x^2 is that right?

    • one year ago
  30. AndrewNJ
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    my first eq is 0.5ab=4x^2 !

    • one year ago
  31. AndrewNJ
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    @FoolForMath yours looks cool! but i think your method could be a bit difficult

    • one year ago
  32. FoolForMath
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    why? I think it's fairly obvious :)

    • one year ago
  33. AndrewNJ
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    well as far as I'm concerned, i seldom use cot sec :(

    • one year ago
  34. AndrewNJ
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    high school in my country didnt teach us cot sec,only taught sin cos and tan

    • one year ago
  35. FoolForMath
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    which country is that?

    • one year ago
  36. AndrewNJ
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    guess it!

    • one year ago
  37. FoolForMath
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    I am very bad at guessing :(

    • one year ago
  38. AndrewNJ
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    alright, it's china!

    • one year ago
  39. radar
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    @AndrewNJ, I am from Missouri, the "show me" state lol, and I would like you to please show me how ab=4x^2 (equation 1 in your first post)

    • one year ago
  40. Yahoo!
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    i also want it @AndrewNJ

    • one year ago
  41. AndrewNJ
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    for 0.5ab is the area of triangle and 0.5*4x*x is also the area of triangle so 0.5ab=0.5*4x*x divide 0.5 in two sides is ab=4x^2

    • one year ago
  42. radar
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    Thanks, you had already shown that, just that, I was being to dense to see it. Thanks again

    • one year ago
  43. radar
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    *to too

    • one year ago
  44. AndrewNJ
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    :)

    • one year ago
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