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Math Help - Right Triangle Trigonomentry

  1. #1
    Junior Member
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    Right Triangle Trigonomentry

    I am having trouble understanding this concept, I would appreciate it if you could help explain this problem.
    The problem uses a right triangle with BC=2 and the angle phata=45, I need to find any missing angles or sides, with the answer to at least 3 decimal digits.
    AB=
    AC=
    B= This is not "B" but the angle of the letter that looks like B but it has a little line that extends below B.

    I hope this is enough information, I looked at my notes and it still is not sinking in.

    Thank you very much!!!!!!
    Keith Stevens
    Kcstevens@ctc.net
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  2. #2
    Member sinewave85's Avatar
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    Quote Originally Posted by kcsteven View Post
    I am having trouble understanding this concept, I would appreciate it if you could help explain this problem.
    The problem uses a right triangle with BC=2 and the angle phata=45, I need to find any missing angles or sides, with the answer to at least 3 decimal digits.
    AB=
    AC=
    B= This is not "B" but the angle of the letter that looks like B but it has a little line that extends below B.

    I hope this is enough information, I looked at my notes and it still is not sinking in.

    Thank you very much!!!!!!
    Keith Stevens
    Kcstevens@ctc.net
    Ok, what you have is a special traingle: 45-45-90 right triangle. All triangles have a sum angle measure of 180 degrees. You know that you have one right angle and one 45 degree angle, so the remaining angle B = 180 - (45 + 90), or 45 degrees. It sould look like this.
    I can't really tell from your description the exact orrientaion of the triangle. But the known side is either the hypotenuse or one of the two legs of equal length. There are several ways to figure this. Let's start with the pythagorean theorum.
    If BC is a leg, then:
    2^{2}+2^{2}=hyp^{2}
    8=hyp^{2}
    \sqrt{8}=hyp
    2\sqrt{2}=hyp
    2.828\approx{hyp}
    If BC is the hyp, then :
    leg^{2}+leg^{2}=2^{2}
    2leg^{2}=4
    leg^{2}=2
    leg=\sqrt{2}
    leg\approx{1.414}
    The other way to do it is to use the law of sines.
     \frac{a}{\sin{A}}=\frac{b}{\sin{B}}=\frac{c}{\sin{  c}}
    Just set it up and solve like any ratio. The last way -- the taking a test and need to work quickly way -- is to know the 1 to 1 to sqrt2 ratio for this type of triangle and just do the mental math.
    If BC is a leg:
    \frac{1}{\sqrt2}=\frac{2}{hyp}
    If BC is the hyp:
    \frac{1}{\sqrt2}=\frac{leg}{hyp}
    Hope this helps!

    P.S. The labels are less important than the orientation, like quick says.
    Last edited by sinewave85; November 16th 2006 at 04:07 PM.
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  3. #3
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by kcsteven View Post
    I am having trouble understanding this concept, I would appreciate it if you could help explain this problem.
    The problem uses a right triangle with BC=2 and the angle phata=45, I need to find any missing angles or sides, with the answer to at least 3 decimal digits.
    AB=
    AC=
    B= This is not "B" but the angle of the letter that looks like B but it has a little line that extends below B.

    I hope this is enough information, I looked at my notes and it still is not sinking in.

    Thank you very much!!!!!!
    Keith Stevens
    Kcstevens@ctc.net
    You have triangle ABC right? is angle phata really angle AB? or is it something else...
    and of course, which side is the hypotenuse.

    EDIT: I suppose the question was already answered
    Last edited by Quick; November 16th 2006 at 06:57 PM.
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