Korzystamy z twierdzenia Pitagorasa:
a² + b² = c²
gdzie:
a,b - przyprostokątne,
c - przeciwprostokątna trójkąta prostokątnego.
e)
[tex]a = 2\sqrt{2}\\\\b = 2\sqrt{2}\\\\c^{2} = a^{2}+b^{2}\\\\c^{2} = (2\sqrt{2})^{2}+(2\sqrt{2})^{2}\\\\c^{2} = 8+8\\\\c^{2} = 16\\\\c = \sqrt{16}\\\\\boxed{c = 4}[/tex]
f)
[tex]a = 2\\\\\frac{1}{b} = 2 \ \ \rightarrow \ \ b = \frac{1}{2}\\\\c^{2} = a^{2}+b^{2}\\\\c^{2}=2^{2}+(\frac{1}{2})^{2}\\\\c^{2} = 4+\frac{1}{4}=\frac{16}{4}+\frac{1}{4} = \frac{17}{4}\\\\c = \sqrt{\frac{17}{4}} = \frac{\sqrt{17}}{\sqrt{4}}\\\\\boxed{c =\frac{\sqrt{17}}{2}}[/tex]
