A group of Boy Scouts on a straight trail headed N30.6° E found the trail led through a briar patch. They chose to walk 156 meters due east along the south edge of the briar patch, then due north along the east edge of the patch back to the trail. How much farther did they walk to avoid walking through the briar patch?
Consider the right triangle △OAB. Given that θ=30.6°,OB=156 m.
Find BA
tan(∠AOB)=OBBA,where ∠AOB=90°−θ Then
BA=OBtan(90°−θ)=OBcotθBA=156cot(30.6°)≈263.78(m) Find OA
cos(∠AOB)=OAOB Then
OA=cos(90°−θ)OB=sinθOB
OB+BA−OA=OB+OBcotθ−sinθOB
OB+BA−OA=OB(1+cotθ−sinθ1)
OB+BA−OA=156(1+cot30.6°−sin30.6°1)≈≈113.32(m) They walked 113.32 m farther to avoid walking through the briar patch.
Comments