Chapter 9 Law of Cosines and Law of Sines Concept #1 The Law of Cosines is used when a triangle has a SSS or a SAS situation . ( This idea was used in proving triangle congruence. Now we use it to analyze which law should be used to solve a triangle. ) Use the law twice always 𝑎 2 = 𝑏 2 + 𝑐 2 −2𝑏𝑐𝐶𝑜𝑠𝐴 𝑏 2 = 𝑎 2 + 𝑐 2 −2𝑎𝑐𝐶𝑜𝑠𝐵 𝑐 2 = 𝑎 2 + 𝑏 2 −2𝑎𝑏𝐶𝑜𝑠𝐶

Use this triangle A b a c B C

Problem #1 Solve the triangle Given 𝑎=20 𝑏=30 𝑐=42

Problem #1 Solve the triangle Given 𝑎=20 𝑏=30 𝑐=42

Problem #2 Solve the triangle Given 𝑎=11 ∠𝐵= 22 ∘ 𝑐=16

Problem #2 Solve the triangle Given 𝑎=11 ∠𝐵= 22 ∘ 𝑐=16

Concept #2 Law of Sines The Law of Sines is used when a triangle has a ASA or a AAS situation . Use the law twice always 𝑎 𝑠𝑖𝑛𝐴 = 𝑏 𝑠𝑖𝑛𝐵 = 𝑐 𝑠𝑖𝑛𝐶

Problem #3 Solve the triangle Given 𝑎=11 ∠𝐵= 22 ∘ ∠𝐶= 77 ∘

Problem #3 Solve the triangle Given 𝑎=11 ∠𝐵= 22 ∘ ∠𝐶= 77 ∘

Problem #4 Solve the triangle Given b=71 ∠𝐵= 34 ∘ ∠𝐶= 100 ∘

Problem #4 Solve the triangle Given b=71 ∠𝐵= 34 ∘ ∠𝐶= 100 ∘

H.W. Law of sine and cosine Worksheets