Answer:
6mm
Step-by-step explanation:
In a right angled triangle if a and b is the length of sides containing right angle, then length of hypotenuse is given by [tex]hypotenuse= \sqrt{a^2 + b^2}[/tex] .
In the given problem a and b are a and 7mm respectively.
hypotenuse = [tex]\sqrt{ 85}[/tex]
Using the formula for hypotenuse we have
[tex]hypotenuse= \sqrt{a^2 + b^2}\\\\\=>\sqrt{85} = \sqrt{a^2 + 7^2} \\ squaring / both / side / we / have\\=>\sqrt{85}^2 = \sqrt{a^2 + 7^2}^2\\=>85 = a^2 + 49\\\\=> a^2 = 85-49 = 36\\=>\sqrt{a^2} = \sqrt{36} \\=> a = 6[/tex]
Thus, length of unknown leg is 6mm.
