Answer:
A. 0.21
Step-by-step explanation:
We have been given a triangle and we are asked to find the value of cos using law of cosines.
Law of cosines:
[tex]c^2=a^2+b^2-2ab*cos(C)[/tex]
Upon substituting our given values in above formula we will get,
[tex]10.9^2=5.8^2+10.5^2-2*5.8*10.5*cos(\theta)[/tex]
[tex]118.81=33.64+110.25-121.8*cos(\theta)[/tex]
[tex]118.81=143.89-121.8*cos(\theta)[/tex]
[tex]118.81-143.89=143.89-143.89-121.8*cos(\theta)[/tex]
[tex]-25.08=-121.8*cos(\theta)[/tex]
[tex]\frac{-25.08}{-121.8}=\frac{-121.8*cos(\theta)}{-121.8}[/tex]
[tex]0.2059113300492611=cos(\theta)[/tex]
Upon rounding our answer to nearest hundredth we will get,
[tex]cos(\theta)\approx 0.21[/tex]
Therefore, the value of [tex]cos(\theta)[/tex] is 0.21 and option A is the correct choice.
