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In triangle ABC, cos A=sqrt frac (7/10) and cos B=sqrt (3/10) Find cos C

 Dec 13, 2023
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We can find cos C using the Law of Cosines:

cos C = (cos^2 A + cos^2 B - 2cos A cos B cos C) / 2

 

Now, plug in the given values:

cos C = ((7/10)^2 + (3/10)^2 - 2 * sqrt(7/10) * sqrt(3/10) * cos C) / 2

 

Simplify the equation:

cos C = (49/100 + 9/100 - 12/100 * cos C) / 2

 

Combine like terms:

cos C = (58/100 - 12/100 * cos C) / 2

 

Multiply both sides by 2 and rearrange:

2 cos C + 12/100 * cos C = 58/100

 

Factor out cos C:

cos C (2 + 12/100) = 58/100

 

Isolate cos C:

cos C = 58/100 * 100 / (200 + 12)

 

Simplify:

cos C = 58/212

 

Therefore, cos C = 29/106.

 Dec 14, 2023

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