Answer:
a = 6.3mm
Step-by-step explanation:
Use Pythagoras theorem here
[tex]a^{2} + b^{2} = c^{2}[/tex]
Rearrange for a by subtracting [tex]b^{2}[/tex] from both sides of the equation
[tex]a^{2} + b^{2} -b^{2} = c^{2} -b^{2}[/tex]
Simplify
[tex]a^{2} = c^{2} -b^{2}[/tex]
Substitute in our numbers and solve for a
[tex]a^{2}[/tex] = [tex]8.3^{2} - 5.4^{2}[/tex]
[tex]a^{2}[/tex] = 68.89 - 29.16
[tex]a^{2}[/tex] = 39.73
a = [tex]\sqrt{39.73}[/tex]
a = 6.3mm
