Presentation on theme: "SOLVING FOR THE MISSING PART OF AN OBLIQUE TRIANGLE"— Presentation transcript:
1SOLVING FOR THE MISSING PART OF AN OBLIQUE TRIANGLE LAW OF SINESSOLVING FOR THE MISSING PART OF AN OBLIQUE TRIANGLE
2An oblique triangle is a triangle that has no right angles. CBAabcTo solve an oblique triangle, you need to know the measure of at least one side and the measures of any other two parts of the triangle – two sides, two angles, or one angle and one side.
3The following cases are considered when solving oblique triangles. Two angles and any side (AAS or ASA)2. Two sides and an angle opposite one of them (SSA)Ccaacb3. Three sides (SSS)3caB4. Two sides and their included angle (SAS)
4If ABC is an oblique triangle with sides a, b, and c, then The first two cases can be solved using the Law of Sines. (The last two cases can be solved using the Law of Cosines.)Law of SinesIf ABC is an oblique triangle with sides a, b, and c, thenCBAbhcaCBAbhcaAcute TriangleObtuse Triangle
5The Law of SinesUse when thegiven info is…ASA or AAS.
6The Law of Sines Start by solving Solve ∆ABC if A = 42º, for the missing angle.Solve ∆ABC if A = 42º,b = 6.4, and C = 81º.B = 180º - 42º - 81ºB = 57º
7The Law of Sines Solve ∆ABC if A = 42º, b = 6.4, and C = 81º. Then solve for one ofthe missing sides.
8The Law of Sines Solve ∆ABC if A = 42º, b = 6.4, and C = 81º. Finally solve for theremaining side.
9Example (SSA): Use the Law of Sines to solve the triangle. A = 110°, a = 125 inches, b = 100 inchesCBAb = 100 inca = 125 in110°21.26°48.74°48.23 inC ≈ 180° – 110° – 48.74°= 21.26°
10Use the Law of Sines to find side b and c. Example (ASA):Find the remaining angle and sides of the triangle.CBAbc60°10°a = 4.5 ftThe third angle in the triangle is A = 180° – A – B= 180° – 10° – 60°= 110°.4.15 ft110°0.83 ftUse the Law of Sines to find side b and c.
11Now, you try some! Solve these triangles. A = 40° B = 20° a = 2 Always draw your triangle before you use the Sine LawNow, you try some!Solve these triangles.A = 40° B = 20° a = 2A = 110° C = 30° c = 33) A = 30° b = C = 50°4) c = 2 A = 40° B = 40°