Hello, blacksuzaku!

The coffee shop is 655 meters from the grocery store,

393 meters from the bookshop, and 314 meters from the tavern.

The bookshop is 236 meters from the tavern and 524 meters from the grocery.

Assuming the distance between the bar and the grocery is less than

the distance between the coffee shop and the grocery,

what is the distance between the bar and the grocery,

rounded to the nearest meter?

If I interpret the question correctly,

. . the tavern is inside the triangle

Since

. . In fact, is a 3-4-5 right triangle. Code:

C
*
|**
| * *
| * *
| * *
| *314 *
393 | * *
| * * 655
| *T *
| * * *
| α *236 x * *
| * θ * *
B *-----------------------* G
524

Let

Use the Law of Cosines in :

. .

. . Hence: .

Use the Law of Cosines in :

. .

Therefore: . m.