Answer
a) $a^2=b^2+c^2-2(b)(c)\cdot $cos$(A)$
b) $a\approx33$ units
Work Step by Step
a) The law of cosine is $a^2=b^2+c^2-2(b)(c)\cdot $cos$(A)$, where $a$, $b$, $c$ are the sides of the triangle and $A$ is the angle opposite of side $a$.
b)
$a^2=30^2+50^2-2(30)(50)\cdot $cos$(40º)$
$a^2=900+2500-3000\cdot 0.77$
$a^2=3400-2298$
$a=\sqrt{1102}\approx33$ units
