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8.1 Classwork Answer Key Formulas βThe Law of Sines Communication a.) What do the lower case letters represent in the triangle? What do the uppercase letters represent in the triangle? Lower case letters represent side length of the triangle. Upper case letters represent angles of the triangle. b.) What case are you given in the triangle described in the verbal/diagram box below? (SSS, SAS, AAS, ASA, SSA)? AAS c.) What are the only cases (SSS, SAS, AAS, ASA, SSA) which you can use the law of Sines? Explain. Verbal/Diagram Directions: Draw and label a diagram that represents the verbal given. C = 102.3° B = 28.7° b = 27.4 ft AAS, ASA, and SSA (the ambiguous case) because all other cases would give you two unknowns in your proportion. Algebraic Directions: Solve for ALL the missing sides and angles of the triangle using the Law of Sines πππππ. π ππππππ. π = ππ. π π π πππππ. π = ππ. π(ππππππ. π) π= ππ. π(ππππππ. π) πππππ. π π = ππ. π ππ -β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β < π© = ππ° -β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β-β πππππ. π πππππ = ππ. π π π πππππ. π = ππ. π(πππππ) ππ. π(πππππ) π= πππππ. π π = ππ. πππ Verbal Two observers are 400 feet apart on opposite sides of a tree. The angles of elevation from the observers to the top of the tree are 14 degrees and 20 degrees. *Note: Do not assume the tree is in the middle of the two observers. Diagram Directions: Draw and label a diagram that represents the real world situation. 146 a b h 14 Algebra Directions: Find the height of the tree. Write your final answer in context of the situation. 400 Communication Directions: Explain your step-βby-βstep thinking process as you went through the problem. 1. Find missing angle in triangle. 2. Find the side length of a or b using Law of Sines. ππππππ πππππ = πππ π π ππππππ = πππ(πππππ) πππ(πππππ) π= ππππππ 3. Use right triangle trigonometry to find the height of the tree. π = πππ. π ππ --------------------------------------------------------------------π πππππ = πππ. π π = πππ. π πππππ π = ππ. π ππ 20
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