7. Applications of Trigonometry

A surveyor wishes to find the distance across a river while standing on a small island. If she measures distances of $a=30m$ to one shore, $c=60m$ to the opposite shore, and an angle of $B=100°$ between the two shores, find the distance between the two shores.

Solve the triangle: $a=5$, $b=15$, $c=13$.

Use the Law of Cosines to find the angle , $C$ rounded to the nearest tenth.

Solve the triangle: $b=5,c=3,A=100°$.