Answer:
11 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex] (Pythagorean Theorem)
[tex]a^{2}[/tex] + [tex]4^{2}[/tex] = [tex](12\frac{1}{3})^{2}[/tex] (square numbers)
[tex]a^{2}[/tex] + 16 = 152 [tex]\frac{1}{9}[/tex] (subtract 16, both sides
[tex]a^{2}[/tex] = 136 [tex]\frac{1}{9}[/tex] (square root both sides)
a = 11 [tex]\frac{2}{3}[/tex] or 11.66 repeating
