$[0/6$ Points$]$

BUELEMPHYS$11.$P$\mathrm{.}035.$

In the sport of orienteering, participants must plan carefully to get from one checkpoint to another in the shortest possible time. In one case, starting at a particular checkpoint, Sam decides to take a straight path that goes west for $710$ meters, and then go northeast for $410$ meters on another straight path to reach the next checkpoint. Northeast, by the way, means $45$ degrees to both north and east.

Between the same two checkpoints, Mary decides to take the shortest distance between the two checkpoints, traveling off the paths through the woods instead.

$($a$)$ What is the distance that Mary travels between the checkpoints? $($Note that Sam travels a total distance of $1120$ m $,$ although his speed is probably significantly higher than Mary's.$)$

m

$($b$)$ In what direction does Mary go$?$ Specify her direction as a positive angle, measured counterclockwise from east.

Update: after looking over similar problems, I keep calculating ~$579\mathrm{.}655$ m which the platform marks as incorrect