Respuesta:
x = 7.86 cm
Explicación paso a paso:
[tex]hipotenusa (c) = 8cm\\cateto(a)=3/2=1.5cm\\cateto(b)=x[/tex]
Teorema de Pitágoras:
[tex]c^{2} =a^{2} +b^{2}[/tex]
Aislamos [tex]b^{2}[/tex]
[tex]b^{2} =c^{2} -a^{2}[/tex]
Sustituimos [tex]b=x[/tex]
[tex]x^{2} =(8)^{2} -(1.5)^{2} =64-2.25[/tex]
[tex]x^{2} =61.75[/tex]
[tex]x=\sqrt{61.75}[/tex]
[tex]x=7.86cm[/tex]
Espero te ayude
