The third angle of the triangle is 180-(70+48)=62 degrees.
We can use the sine rule:
a/sin70=b/sin48=(110-(a+b))/sin62 because we know the perimeter is 110mm.
From this a/sin70=(110-(a+b))/sin62.
Cross-multiply: asin62=(110-(a+b))sin70=110sin70-asin70-bsin70.
a(sin62+sin70)=(110-b)sin70; a=(110-b)sin70/(sin62+sin70).
But a=bsin70/sin48, therefore bsin70/sin48=(110-b)sin70/(sin62+sin70).
Therefore: b/sin48=(110-b)/(sin62+sin70).
Cross-multiply: bsin62+bsin70=110sin48-bsin48, b(sin62+sin70+sin48)=110sin48.
Therefore b=110sin48/(sin62+sin70+sin48)=31.86mm approx.
Since a=bsin70/sin48, a=110sin70/(sin62+sin70+sin48)=40.29mm approx and the third side=37.85mm.
The third side is the base and the angles at each end of the base can be constructed to form the other two sides.