Answer
$A\approx38^\circ, B\approx61^\circ, C\approx81^\circ$
Work Step by Step
Step 1. With the given numbers, we have
$a=BC=4.3+3.0=7.3, b=AC=7.5+3.0=10.5,c=AB=7.5+4.3=11.8$
Step 2. Using the Law of Cosines, we have
$c^2=a^2+b^2-2ab\ cosC$ or $11.8^2=7.3^2+10.5^2-2(7.3)(10.5)\ cosC$
which gives
$cosC\approx0.1585$ and $C=acos(0.1585)\approx81^\circ$
Step 3. Using the Law of Sines, we have
$\frac{sinA}{a}=\frac{sinC}{c}$ and $sinA=\frac{7.3sin(81^\circ)}{11.8}\approx0.6110$
thus
$A=asin(0.6110)\approx38^\circ$ and $B\approx180^\circ-81^\circ-38^\circ=61^\circ$
Step 4. The solutions are
$A\approx38^\circ, B\approx61^\circ, C\approx81^\circ$
