Law of sines 6-1

Law of Sines 𝑎 sin 𝐴 = 𝑏 sin 𝐵 = 𝑐 sin 𝐶 Where side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C Use whenever you know a corresponding side and angle.

Triangle congruence theorems AAS ASA SSA ASS Note: whenever you have two angles, find the third.

Example Solve the triangle C = 102.3°, B = 28.7°, b = 27.4 ft

Example A pole tilts toward the sun at an 8° angle from vertical, and it casts a shadow 22 ft long. The angle of elevation from the tip of the shadow to the top of the pole is 43°. How tall is the pole?

Ambiguous case ASS should stand out. If the side opposite the angle is longer than the adjacent side there is only one possible triangle. If it is shorter, there are two triangles (one acute, one obtuse). The law of sines will give you the acute first. If you subtract the angle you find from 180, you find the obtuse triangle.

Example Solve the triangle: a = 22 in, b = 12 in, A = 42°

Example Solve the triangle: a = 15, b = 25, A = 85°

Example Solve the Triangle: a = 12, b = 31, A = 20.5°