SOLUTION: In ΔABC, if the length of sides a, b, and c are 3.5 centimeters, 5.5 centimeters, and 6 centimeters respectively, what is m∠C to two decimal places?

Algebra ->  Trigonometry-basics -> SOLUTION: In ΔABC, if the length of sides a, b, and c are 3.5 centimeters, 5.5 centimeters, and 6 centimeters respectively, what is m∠C to two decimal places?       Log On


   

Question 1207309: In ΔABC, if the length of sides a, b, and c are 3.5 centimeters, 5.5 centimeters, and 6 centimeters respectively, what is m∠C to two decimal places?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


a=3.5
b=5.5
c=6
find m < C

use the law of cosine

c%5E2+=+a%5E2+%2B+b%5E2+-+2ab+%2Acos%28C%29......substitute given values
6%5E2+=+3.5%5E2+%2B+5.5%5E2+-+2%2A3.5%2A5.5+%2Acos%28C%29
36+=+12.25+%2B+30.25+-38.5+%2Acos%28C%29
36+=+42.5+-38.5+%2Acos%28C%29
38.5+%2Acos%28C%29=+42.5+-36
38.5+%2Acos%28C%29=+6.5
cos%28C%29=+6.5%2F38.5
cos%28C%29=+0.1688311688311
C=cos%5E-1%280.1688311688311%29
C=1.4011526325293...(result in radians)
C=80.28013°