How far is point B from the fire?

Question

Point B is 9 miles east of point A. Point a  is 11 degrees 40 minutes north east from the fire. Point B is 28 degrees 40 minutes north east from the fire.

Answer 1

This one's pretty hard to answer without graph but the arrangement of the points will be like this:

 

                                 A                                  B

 

 

 

 

 

 

               FIRE

 

 

When dealing with bearing, most of the time our reference is North and South. (The exception is if it's in a form of example: North of East, which is very specific on what should be your reference)

 

Again, this is hard without graph, but by making that a triangle you would end up with Angle FIRE to be 17º (that is 28º40' - 11º40').

 

The Angle A would be 11º40' (observe alternate interior angle of parallel lines) + 90º = 101º40'. You can observe this in the graph.

 

The Angle B would just be 180º - Angle A - Angle FIRE = 61º20'

 

Let:

a = distance from B to FIRE

fire = distance from A to B

 

We can just use Sine Law to solve:

 

fire/sin(FIRE) = a/sin(A)

 

9/sin(17º) = a/sin(101º40')

 

a = 30.15 miles