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Math Help - Trigonometry to seld complex shapes

  1. #1
    Junior Member turbod15b's Avatar
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    Trigonometry to seld complex shapes

    how do i work out the angles for A, B and C

    all in mm


    cheers

    also how do i find the angles A & B in this triangle ?

    is it 20cos60?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by turbod15b View Post
    how do i work out the angles for A, B and C

    all in mm


    cheers

    also how do i find the angles A & B in this triangle ?

    is it 20cos60?
    For the first triangle use either the Law of Sines or the Law of Cosines:
    Law of Sines:
    sin(angle A)/a = sin(angle B)/b = sin(angle C)/c
    where a, b, and c are the sides across the triangle from angles A, B, and C respectively.

    Law of Cosines:
    a^2 = b^2 + c^2 - 2bc*cos(angle A)
    b^2 = a^2 + c^2 - 2ac*cos(angle B)
    c^2 = a^2 + b^2 - 2bc*cos(angle C)

    For the second triangle, is what "20cos60?"

    By definition of the sine and cosine of an angle we have that
    sin(angle B) = 20/60 ==> angle B = asn(1/3) = 19.4712 degrees
    and
    cos(angle A) = 20/60 ==> angle A = acs(1/3) = 70.5288 degrees

    As a quick check, note that the sum of these two angles is 90 degrees, as it should be for a right triangle.

    -Dan
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  3. #3
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    Hello, turbod15b!


    The first problem has: .a = 31, b = 27, c = 37.

    Given no angles, we must use variations of the Law of Cosines.


    . . . . . . . b + c - a . . .27 + 37 - 31
    cos A .= .-------------- .= .------------------- .= .0.569069069
    . . . . . . . . . .2bc . . . . . . . . 2(27)(37)

    Hence: .A .= .55.31466541 . . . . A . .55.3


    . . . . . . . a + c - b . . .31 + 37 - 27
    cos B .= .-------------- .= .------------------- .= .0.697907585
    . . . . . . . . . .2ac . . . . . . . . 2(31)(37)

    Hence: .B .= .45.74063061 . . . . B . .45.7


    Then: .C .= .180 - 55.3 - 45.7 . . . . C .= .79.0

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    If you have time, check angle C by using the Law of Cosines . . .

    . . . . . . . a + b - c . . . 31 + 27 - 37
    cos C .= .--------------- .= .------------------ .= .0.191756272
    . . . . . . . . . 2ab . . . . . . . . .2(31)(27)

    Hence: .C .= .78.94470398 . . . . C . .78.9 .close enough!

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  4. #4
    Junior Member turbod15b's Avatar
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    i dont understand how u get

    Cos A = 0.569069069

    Cos B = 0.697907585

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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by turbod15b View Post
    i dont understand how u get

    Cos A = 0.569069069

    cos(A):
    26^2 + 37^2 - 31^2 = 1137
    2*27*37 = 1998

    cos(a) = 1137/1998 = 0.569069

    Now you try cos(B).

    -Dan
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  6. #6
    Junior Member turbod15b's Avatar
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    31^2+37^2-27^2=1601
    2*31*37=2294

    1601/2294=0.697907585

    i get that bit, but i dont get how u get it to

    Hence: .A .= .55.31466541 . . → . . A .≈ .55.3

    Hence: .B .= .45.74063061 . . → . . B .≈ .45.7
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by turbod15b View Post
    31^2+37^2-27^2=1601
    2*31*37=2294

    1601/2294=0.697907585

    i get that bit, but i dont get how u get it to

    Hence: .A .= .55.31466541 . . → . . A .≈ .55.3

    Hence: .B .= .45.74063061 . . → . . B .≈ .45.7
    Oh! Sorry.

    Your calculator probably has a "2nd" key or something like it. You need to plug in the 0.569069069, and hit "2nd cos" (to get to the function above the "cos" button.) This is the inverse cosine function and should give you the correct answer. If it does not, then you are likely in "radian" mode and need to learn how to change your calculator into "degree" mode.

    -Dan
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  8. #8
    Junior Member turbod15b's Avatar
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    thanks

    my second buttons are shift sin-1, cos-1,tan-1
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