Question

Find indicated measure, round to the nearest tenth. Use law of cosines. Question 10.

Answer 1

Problem N 10

step 1

Find out the length of the side AC

Applying the law of cosines

$AC^2=BC^2+BA^2-2(BC)(BA)cosB$

substitute given values

$\begin{gathered} AC^2=29^2+24^2-2(29)(24)cos101^o \\ AC=41 \end{gathered}$

step 2

Find out the measure of the angle C

Applying the law of cosines

$AB^2=CB^2+CA^2-2(CB)(CA)cosC$

substitute given values

$\begin{gathered} 24^2=29^2+41^2-2(29)(41)cosC \\ solve\text{ for cosC} \\ cosC=\frac{29^2+41^2-24^2}{2(29)(41)} \\ \\ C=35.1^o \end{gathered}$

The measure of the angle C is 35.1 degrees