(TRIG)I need step by step help with these trig problems?

Solve the triangle with the given information

1. a=6.8

b=13.0

c.16.6

2. β=63.5°

a=12.20

c=7.80

2 Answers

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  • 1 decade ago
    Favorite Answer

    I assume you must find all the angles.

    Start with the biggest side and find the angle opposite it.

    16.6 ^2 = 13^2 + 6.8^2 - 2(13)(6.8) cos A

    275.56=169 + 46.27 - 176.8cosA

    60.29 = -176.8 cos A

    -.3410 = cos A

    A = 110

    Now do Law of Sines to get next biggest angle

    16.6/sin 110 = 13/sin A

    13 sin 110 = 16.6 sin A

    .

    .7359 = sin A

    A = 47

    Now to find the last angle 180-47-110 = 23

    Problem 2

    You can find the side opposite B by doing law of cosines

    b^2 = 7.8^2 + 12.2^2 - 2(7.8)(12.2)cos63.5

    b^2 = 60.84 + 148.84 - 84.92

    b^2 = 124.76

    b = 11.2

    NOw do Law of SInes to find the second biggest angle

    11.2/sine 63.5 = 12.20/sin a

    sin a = .9748

    a = 77

    Now 180 - 63.5-77 = third angle of 39.5

  • Anonymous
    1 decade ago

    1. a^2 = b^2 + c^2 - 2bccosA

    cos A = (b^2 + c^2 - a^2)/2bc = .923

    A = 22.60 degrees.

    cos B = (c^2 + a^2 - b^2)/2ca = .679

    B = 47.40 degrees.

    cosC = (a^2 + b^2 - c^2)/2ab = -.3515

    C = 110 degrees

    Check: 22.6 + 47.4 + 110 = 180

    2. b^2 = c^2 + a^2 - 2ca cosB = 124.76

    b = 11.17

    cos A = (b^2 + c^2 - a^2)/2bc = .211

    A = 77.8 deg

    C = 180- 77.8 - 63.5 = 38.7 deg

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