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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

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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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