A brother and sister are playing in the woods, when suddenly the brother realize

Question

A brother and sister are playing in the woods, when suddenly the brother realizes that they are separated. The last place he remembers seeing his sister is at a particularly large tree. The brother traveled

A brother and sister are playing in the woods, when suddenly the brother realizes that they are separated. The last place he remembers seeing his sister is at a particularly large tree. The brother traveled d1=22.5 m at ?1=20.0? from the tree then turned and traveled d2=12.0 m at ?2=130?. Meanwhile, the sister traveled d3=19.0 m at an angle of ?3=?117? from the tree. The angles are given with respect to east with counterclockwise being defined as positive

Explanation / Answer

initially assume both are at origin .

D1= (22.5cos20 , 22.5sin20).

D2 = (22.5cos20+12cos130 , 22.5sin20+12sin130)

       =(13.43 , 16.89)

displacement of the boy relative to the tree D = sqrt(13.43^2 + 16.89^2) = 21.58

angle theta = tan^(-1) (16.89/13.43) = 51.5 deg

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