Answer:
20 units
Step-by-step explanation:
Consider right triangle ABD. In this triangle,
[tex]BD=37\ un.\\ \\AD=19+16=35\ un.[/tex]
By the Pythagorean theorem,
[tex]BD^2=AD^2+AB^2\\ \\37^2=35^2+AB^2\\ \\AB^2=37^2-35^2=(37-35)(37+35)=2\cdot 72=144\\ \\AB=12\ un.[/tex]
Consider right triangle ABC. In this triangle,
[tex]AC=16\ un.\\ \\AB=12\ un.[/tex]
By the Pythagorean theorem,
[tex]BC^2=AB^2+AC^2\\ \\BC^2=16^2+12^2\\ \\BC^2=256+144=400\\ \\BC=20\ un.[/tex]
