Answered By Eric C

This question deals with application of the Sine Law:

 $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$asinA =bsinB =csinC  

Given b=8cm, c=10 and B=35 degrees, we can solve for the angle C by using the Sine Law:

 $\frac{8cm}{\sin35}=\frac{10cm}{\sin C}$8cmsin35 =10cmsinC  

 $\sin C=10cm\cdot\frac{\sin35}{8cm}=0.71697...$sinC=10cm·sin358cm =0.71697...

  $C=\sin^{-1}\left(0.71697\right)=45.8^{\circ}$‍C=sin⁻¹(0.71697)=45.8^? 

Knowing that the sum of the angles in a triangle equals 180 degrees we can find the final angle A, and using the Sine Law again, find length a:

 $A=180^{\circ}-B-C=180^{\circ}-35^{\circ}-45.8^{\circ}=99.2^{\circ}$A=180^?−B−C=180^?−35^?−45.8^?=99.2^? 

 $a=\sin A\cdot\frac{b}{\sin B}=\sin99.2\cdot\frac{8cm}{\sin35}=13.77cm$a=sinA·bsinB =sin99.2·8cmsin35 =13.77cm