how do i do word problems with radicals in them?

Question

a car travels 28 miles north and then turns east. How far did the car travel east if the destination is 53 miles from the starting point?

Answer 1

Mary,

          Let's say the car travels n miles north and then turns east ( 90 degree turn) and travels e miles east. We want to be r miles from the starting point.

          Each leg of the trip is part of a right triangle. The sides of a right triangle obeys r²=n²+e² we know r and n i.e. r=53 and n=28 so we can solve for  e as e=(r²-n²)^1/2  =(53²-28²)^1/2= 45. So the car must have driven 45 miles east.

 

^Jim