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AB = 8 cm, AC = 6 cm, AD = 7 cm, CD = 2.82 and CAB=50°. Find the length BC, angle ABC, angle CAD , area of triangle ACD

  • math -

    Start off with the cosine law to find BC
    BC^2= 8^2 + 6^2 - 2(8)(6)cos50°
    ..
    ..
    BC = 6.188

    Now use the sine law to find angle B

    For angle CAD, use the cosine law again
    7^2 = 6^2 + 2.82^2 - 2(6)(2.82)cos C
    cos C = -.14916..
    angle C = 98.578°

    to find the area of a triangle use
    area = (1/2)ab sin Ø , where Ø is the contained angle between sides a and b
    I would use angle C as that contained angle and sides 6 and 2.82

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