Points A and B are separated by a lake To find the distance

Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such than CAB = 48.4 degree. Find the distance across the lake from A to B.

Solution

by law of sines for the triangle ABC

BC/sin(A) =AC/sin(B)

461/sin48.4^o =331/sin(B)

sin(B)=(331/461)sin48.4^o

sin(B)=0.5369

B=32.474⁰

A+B+C=180^o

48.4+32.474+C=180

C=99.1^o

by law of sines for the triangle ABC

BC/sin(A) =AB/sin(C)

461/sin48.4^o =AB/sin(99.1^o)

AB=461*(sin99.1^o)/(sin48.4^o)

AB=608.7

Distance AB=608.7 yards