Question

Find each measure to the nearest tenth using law of cosine. Number 9.

Answer 1

Problem N 9

step 1

Find out the length of the side AB

Applying the law of cosines

we have that

$AB^2=BC^2+AC^2-2(BC)(AC)cosC$

substitute given values

$\begin{gathered} AB^2=29^2+28^2-2(29)(28)cos52^o \\ AB=25 \end{gathered}$

step 2

Find out the measure of angle A

Applying the law of cosines again

$BC^2=AB^2+AC^2-2(AB)(AC)cosA$

substitute given values

$\begin{gathered} 29^2=25^2+28^2-2(25)(28)cosA \\ solve\text{ for cosB} \\ cosA=\frac{25^2+28^2-29^2}{2(25)(28)} \\ \\ A=66.1^o \end{gathered}$

The measure of angle A is 66.1 degrees