a)
Z zależności boków w trójkącie prostokątnym o kątam ostrych 30° i 60° mamy:
c = 2a = 10 cm
a = 5 cm
b = 5√3 cm
Obw = a + b + c
Obw = 5 + 5√3 + 10 = 15 + 5√3 = 5(3 + √3) cm
b)
[tex]c = 5 \ cm\\\\a^{2}+a^{2} = 5^{2}\\\\2a^{2} = 25 \ \ /:2\\\\a^{2} = \frac{25}{2}\\\\a = \frac{\sqrt{25}}{\sqrt{2}} = \frac{5}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}} = \frac{5\sqrt{2}}{2}\\\\b = a = \frac{5\sqrt{2}}{2}\\\\Obw = a+b+c\\\\Obw = \frac{5\sqrt{2}}{2}+\frac{5\sqrt{2}}{2}+5 = 5\sqrt{2}+5} = 5(\sqrt{2}+1) \ cm[/tex]
