Law of Sines Objective: To solve triangles that are not right triangles

Law of Sines We have been solving for sides and angles of right triangles with a variety of methods. We will now look at solving triangles that are not right triangles. These triangles are called oblique triangles.

Law of Sines We have been solving for sides and angles of right triangles using a variety of methods. We will now look at solving triangles that are not right triangles. These triangles are called oblique triangles. To solve an oblique triangle with the Law of Sines, you need to know the measure of at least one side and the opposite angle. This breaks down into the following cases.

Law of Sines To use the Law of Sines, you need to have: 1.Two angles and any side (AAS or ASA) 2.Two sides and an angle opposite one of them (SSA)

Law of Sines Given triangle ABC with sides a, b and c, then:

Example 1(AAS) For the given triangle, find the remaining angle and sides.

You Try Given triangle ABC, find the missing angle and sides.

Example 2(ASA) A pole tilts toward the sun at an 8 0 angle from the vertical, and it casts a 22-foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is How tall is the pole?

You Try Given triangle ABC, find the missing angle and sides. <A = 70 0 <B = 44 0 c = 12 ft

Example 3 We know from Geometry that SSA does not make a unique triangle. When given SSA, one of three situations may occur. 1.One unique triangle 2.No triangle 3.Two different triangles

Example 3 For the given triangle, find the missing angles and side.

Example 4 For the given triangle, find the missing angles and side. a = 12m b = 31m <A =

Practice Pg. 347 and 348 (3 – 17odd)