Please check the attached question for a better understanding of the solutions provided here.
In the attached diagram, North is shown straight up. The rest of the cardinal directions follow.
Your current position is depicted by the letter P.
Your friend's current position after a walk of 205 yards due west from your position is depicted by the letter F.
The location of the cabin (which happens to be due north from your current position) is depicted by the letter C.
The bearing on the cabin from F is of N23.9°E which too is shown in the diagram. Thus, [tex] \angle PFC=23.9^0 [/tex]
It is clear from the question that we have to find the distance of the Cabin C from your current position P. Thus, we have to find PC=x.
By using the definition of the definition of the tan ratio, we get:
[tex] tan(\angle PFC)=\frac{Perpendicular}{Base}=\frac{PC}{FP} [/tex]
[tex] tan(23.9^0)=\frac{x}{205} [/tex]
[tex] \therefore x=205\times tan(23.9^0)\approx90.8 [/tex] yards.
Thus, your are, approximately, 90.8 yards away from the cabin.
