Hello, Juan!

I'll explain

. . The means we start by facing *North.*

. . Then means we turn *to the west.*

And __that__ is the direction indicated by .

Similarly, means: face South, turn 30° to the east.

Code:

F * - - - - - - - * A
\ |
\ |
\ |
d \ | 8.6
\ |
\ θ |
\ |
* B

The fire is at . .Angle . .Let

In right triangle , we have: .

Therefore: . miles.

Solve for

Here's a back-door approach to this problem . . .

If , then and are complementary: .

Look at this right triangle. Code:

* B
c * *
* * a
* *
A * * * * * C
b

We have: . .and .

See? . . . Angles and are from the *same right triangle.*

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Back to the problem: .

Since and are complementary: .

Therefore: .

Note: TPHacker's solution is __complete__.