Answer:
6 mm
Step-by-step explanation:
Use the Pythagorean Theorem to solve for the unknown leg
[tex]a^{2} +b^{2}=c^{2}[/tex]
Since we need to solve for a, we will manipulate the equation in terms of b and c → [tex]a=\sqrt{c^{2}-b^{2} }[/tex]
Here, b = 7 mm and c = [tex]\sqrt{85}[/tex] mm
Plugging these numbers into our equation gives us [tex]a=\sqrt{(\sqrt{85})^{2} -(7)^{2} }[/tex] →[tex]\sqrt{85-49}[/tex] = [tex]\sqrt{36}[/tex] = 6 mm
