Answer to Question #104462 in Trigonometry for Antoni Perez

Question

In the San Gabriel Mountains in California, lookout station Running Deer is 18 kilometers due west of station Lazy Bear. The bearing from Running Deer to a fire directly south of Lazy Bear is S38.4°E. To the nearest tenth of a kilometer, how far is the fire from Running Deer? From Lazy Bear?

Answer 1

Station Running Deer, station Lazy Bear and fire lie at the vertices of a right-angled triangle. Distance from Running Deer to Fire is:

AB=AC/sin(38.4°)=28.9

Distance from Lazy Bear to fire:

BC=AC/tan(38.4°)=22.7