Answer: AB=21.88 mm, BC=51.54 mm
Step-by-step explanation:
Given
[tex]\angle A=67^{\circ}[/tex]
[tex]AC=56\ mm[/tex]
The other two sides can find out using trigonometry
[tex]\Rightarrow \sin 67^{\circ}=\dfrac{BC}{AC}\\\\\Rightarrow \sin 67^{\circ}=\dfrac{BC}{56}\\\\\Rightarrow BC=56\sin 67^{\circ}\\\Rightarrow BC=51.54\ mm[/tex]
Similarly, for AB
[tex]\Rightarrow \cos 67^{\circ}=\dfrac{AB}{AC}\\\\\Rightarrow \cos 67^{\circ}=\dfrac{AB}{56}\\\\\Rightarrow AB=56\cos 67^{\circ}\\\Rightarrow AB=21.88\ mm[/tex]
Angle C is given by
[tex]\angle C=90^{\circ}-67^{\circ}\\\angle C=23^{\circ}[/tex]