Odpowiedź:
1. Z twierdzenia Pitagorasa - a² + b² = c², gdzie a i b to przyprostokątne, a c to przeciw prostokątna.
a) 4² + 2² = c²
16 + 4 = c²
c² = 20
c = [tex]\sqrt{20}[/tex] = [tex]\sqrt{4x5}[/tex] = 2[tex]\sqrt{5}[/tex]
b) a² + 5² = 20²
a² + 25 = 400
a² = 375
a = [tex]\sqrt{375}[/tex] = [tex]\sqrt{15x25}[/tex] = 5[tex]\sqrt{15}[/tex]
c) 20² + b² = 34²
400 + b² = 1156
b² = 756
b = [tex]\sqrt{756}[/tex] = [tex]\sqrt{36x21}[/tex] = 6[tex]\sqrt{21}[/tex]
2. Z twierdzenia Talesa: [tex]\frac{4}{x}[/tex] = [tex]\frac{5}{6}[/tex]
4 = [tex]\frac{5}{6}[/tex]x
24 = 5x
x = [tex]\frac{24}{5}[/tex] = 4[tex]\frac{4}{5}[/tex]
