Answer:
A) [tex]\sqrt{146}[/tex]
Step-by-step explanation:
The Pythagorean Theorem states that for a right triangle with side lengths [tex]a[/tex] and [tex]b[/tex], and a hypotenuse of [tex]c[/tex], the equation that relates to every side of the triangle is [tex]a^2+b^2=c^2[/tex].
In this case, we'll let [tex]a=\sqrt{82}\:\text{mi}[/tex] and [tex]b=8\:\text{mi}[/tex], and we can solve for the hypotenuse [tex]x[/tex]:
[tex]a^2+b^2=c^2\\\\\sqrt{82}^2+8^2=x^2\\\\82+64=x^2\\\\146=x^2\\\\\sqrt{146}=x[/tex]
Therefore, the missing side of the triangle is [tex]\sqrt{146}\: \text{mi}[/tex].
