${\left|AE\right|}^2+{\left|AB\right|}^2={\left|BE\right|}^2$

${\left|AE\right|}^2+{27}^2={45}^2$  

${\left|AE\right|}^2+729=2025\mid -729$  

${\left|AE\right|}^2=1296\mid \sqrt{}$  

$\left|AE\right|=36$  

 

${\left|AC\right|}^2+{20}^2={52}^2$  

${\left|AC\right|}^2+400=2704\mid -400$  

${\left|AC\right|}^2=2304\mid \sqrt{}$  

$\left|AC\right|=48$  

 

${\left|AC\right|}^2+{\left|AE\right|}^2={\left|CE\right|}^2$  

${36}^2+{48}^2={\left|CE\right|}^2$  

$1296+2304={\left|CE\right|}^2$  

${\left|CE\right|}^2=3600\mid \sqrt{}$  

$\left|CE\right|=60$  

Odp. Odległość między punktami A i C wynosi 60.