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anonymous

  • 5 years ago

right triangle has angle A and B. Cos B=3/4 the hypotenuse is 5. find x (opposite) and y (adjacent) the B is above the 90 degrees, and A is next to it (sorry hard to explain cause there's a drawing)

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  1. Yuki
    • 5 years ago
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    x = 4 and y =3

  2. Yuki
    • 5 years ago
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    ops, my mistake

  3. dumbcow
    • 5 years ago
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    cosB = adj/hyp = y/5 cosB = 3/4 --> y/5 = 3/4 y=(3*5)/4 = 15/4 use pythagorean theorem to find x 5^2 = (15/4)^2 + x^2 x^2 = 25 -(225/16) x^2 = (400 - 225)/16 x = 5*sqrt(7)/4

  4. Yuki
    • 5 years ago
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    if the hypotenuse is 5, then cos(B) = opposite / hypotenuse = opp / 5 so 3/4 = opp / 5 by multiplying 5 on both sides, opp = 15/4

  5. dumbcow
    • 5 years ago
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    haha i almost made same mistake when i saw 3/4 :)

  6. Yuki
    • 5 years ago
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    now if you want to find the adj, you use sin(B) or just use the pythagorean thm. \[5^2 = (15/4)^2 + adj^2\] or sin(B) = sqrt(7) so sin(B) = opposite / hypotenuse = opp / 5 = sqrt(7) so opp =\[5\sqrt{7}\]

  7. Yuki
    • 5 years ago
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    I'm making so much mistakes today... sorry for cos(B) it is actually adj / hyp so the adjacent side is 15/4

  8. anonymous
    • 5 years ago
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    haha. yeah. it's okay, dumbcow explained it. now what if i wanted to find sin(B) would it be (5*sqrt7/4)/5 ?

  9. Yuki
    • 5 years ago
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    sin(b) =\[\sqrt{1-\cos^2(B)}\] so it is \[\sqrt{7/4}\]

  10. Yuki
    • 5 years ago
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    sqrt(7) / 4

  11. anonymous
    • 5 years ago
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    thanks everybody! =]

  12. Yuki
    • 5 years ago
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    メダルくれたら嬉しいんだけど。

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