9-3 L AW OF S INES

L AW OF S INES A B Given an oblique triangle (no right angle) we can draw in the altitude from vertex B Label the altitude k and find two equations involving k C a b c k

L AW OF S INES By using the equations for the area of a triangle. We can obtain the equation for the Law of Sines by dividing everything by

L AW OF S INES In triangle ABC the following is true What are we given? AAS or ASA Two angles and any side (1 possible triangle) SSA Two sides and an angle opposite from one of them (ambiguous case: may not be a solution, 1 or 2 solutions)

EXAMPLE #1 A civil engineer wants to determine the distances from points A and B to an inaccessible point C. From direct measurement the engineer knows that AB=25m, <A=110°, and <B=20°. Find AC and BC. 110° 25m A C B a b 20°

EXAMPLE #2 In triangle RST, <S=126°, s=12, and t=7. Determine whether <T exists. If so, find all possible measures of <T.

E XAMPLE #3 Solve triangle RST is <S=40°, r=30, and s=20. Give angle measure to the nearest tenth of a degree and lengths to the nearest hundredth.

E XAMPLE #4 Solve triangle ABC when <C=112°, c=5, and a=7.

E XAMPLE #4 Solve triangle ABC when <A=30°, a=7, and c=16.