Answer
$A\approx51^\circ, B\approx61^\circ, C\approx68^\circ$
Work Step by Step
Step 1. With the given numbers, we have
$a=BC=4+3.5=7.5, b=AC=5+3.5=8.5,c=AB=5+4=9$
Step 2. Using the Law of Cosines, we have
$c^2=a^2+b^2-2ab\ cosC$ or $9^2=7.5^2+8.5^2-2(7.5)(8.5)\ cosC$
which gives
$cosC=0.3725$ and $C=acos(0.3725)\approx68^\circ$
Step 3. Using the Law of Sines, we have
$\frac{sinA}{a}=\frac{sinC}{c}$ and $sinA=\frac{7.5sin(68^\circ)}{9}\approx0.7727$, thus $A=asin(0.7727)\approx51^\circ$ and $B\approx180^\circ-68^\circ-51^\circ=61^\circ$
Step 4. The solutions are
$A\approx51^\circ, B\approx61^\circ, C\approx68^\circ$
