Question

In Fayetteville, the library is 3 miles due west of the post office and the zoo is 5 miles due north of the library. What is the distance from the post office to the zoo?

Answer 1

`√(34)\approx 5.8\ mi`

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,

`ZP^2 =PL^2 +LZ^2,\\ \\ZP^2 =3^2+5^2,\\ \\ZP^2=9+25=34,\\ \\ZP=√(34)\approx 5.8\ mi.`