Problem N 10
step 1
Find out the length of the side AC
Applying the law of cosines
[tex]AC^2=BC^2+BA^2-2(BC)(BA)cosB[/tex]
substitute given values
[tex]\begin{gathered} AC^2=29^2+24^2-2(29)(24)cos101^o \\ AC=41 \end{gathered}[/tex]
step 2
Find out the measure of the angle C
Applying the law of cosines
[tex]AB^2=CB^2+CA^2-2(CB)(CA)cosC[/tex]
substitute given values
[tex]\begin{gathered} 24^2=29^2+41^2-2(29)(41)cosC \\ solve\text{ for cosC} \\ cosC=\frac{29^2+41^2-24^2}{2(29)(41)} \\ \\ C=35.1^o \end{gathered}[/tex]
The measure of the angle C is 35.1 degrees
