Answer:
[tex]\sqrt{34}\approx 5.8\ mi[/tex]
Step-by-step explanation:
Let point P be the post office, L - library and Z - zoo. Consider rightt triangle PLZ with right angle at vertex L. In this triangle, legs PL=3 mi and LZ=5 mi. By the Pythagorean theorem,
[tex]ZP^2 =PL^2 +LZ^2,\\ \\ZP^2 =3^2+5^2,\\ \\ZP^2=9+25=34,\\ \\ZP=\sqrt{34}\approx 5.8\ mi.[/tex]
