Answer
$\angle A=180-\left( 29+52\right) =99$
$\left| AB\right| =\dfrac {43\sin 29}{\sin 99}\approx 21.1;$
$\left| AC\right| =\dfrac {43\sin 52}{\sin 99}\approx 34.3$
Work Step by Step
Sum of internal angles of triangle is $180^0$ then
$\angle A=180-\left( 29+52\right) =99$
From the law of sines
$\dfrac {43}{\sin \angle A}=\dfrac {\left| AB\right| }{\sin 29}\Rightarrow \left| AB\right| =\dfrac {43\sin 29}{\sin 99}\approx 21.1;$
$\left| AC\right| =\dfrac {43\sin 52}{\sin 99}\approx 34.3$
