Question

respondem pra mim, por favor

Answer 1

 Olá Luh,
boa noite!

 Note que o triângulo é rectângulo, com isso, podemos fazer,

a)

$\tan30^o=\frac{\overline{AO}}{\overline{PA}}\\\\\frac{\sqrt{3}}{3^{\div(3}}=\frac{r}{18^{\div(3}}\\\\\frac{\sqrt{3}}{1}=\frac{r}{6}\\\\\boxed{r=6\sqrt{3}\,\text{cm}}$


 Para encontrar o valor de "x", podemos aplicar o Teorema de Pitágoras, veja:

b)

$(\overline{PO})^2=(\overline{PA})^2+(\overline{AO})^2\\\\x^2=(18)^2+(6\sqrt{3})^2\\\\x^2=324+108\\\\x^2=432\\\\x^2=16\cdot9\cdot3\\\\x=\sqrt{16\cdot9\cdot3}\\\\x=4\cdot3\sqrt{3}\\\\\boxed{x=12\sqrt{3}\,\text{cm}}$

 Espero ter ajudado!!