Report

7.1 Law of Sines Day 1 Tues Feb 10 Do Now Let Triangle ABC be a right triangle where angle C is 90 degrees, angle B is 37.1 degrees, and side BC is 6.3 Solve the triangle Quiz Review • Retakes by Solving Triangles • To solve a triangle means to find the lengths of all its sides and the measures of all its angles • We’ve solved right triangles previously Oblique Triangles • A triangle that is not a right triangle is considered oblique • Oblique triangles can be solved if at least one side and any other 2 measures (length or angle) are known Law of Sines • Proof Law of Sines • In any triangle ABC, sin A sin B sinC = = a b c Where side a is opposite of angle A, etc Law of Sines notes • When solving triangles, there is a possibility that you can have one solution, two solutions, or no solution. • This depends on the equations you set up – Remember, the range of sinx is [-1, 1] Ex1 • In triangle EFG, e = 4.56, E = 43deg, G = 57 deg • Solve the triangle Ex3 • In Triangle QRS, q = 15, r = 28, Q = 43.6 deg • Solve the triangle Ex 4 • In triangle XYZ, x = 23.5, y = 9.8, X = 39.7 deg • Solve the triangle Ex5 • In triangle ABC, b = 15, c = 20, B = 29 deg • Solve the triangle Closure • Solve the triangle ABC, if possible • A = 131 deg, C = 23 deg, b = 10 • HW: p.608 #1-15 odds 7.1 Law of Sines Day 2 Wed Feb 11 • Do Now • In triangle ABC, B = 115deg, c = 45.6 yd, b = 23.8 yd. Solve the triangle HW Review: p.608 #1-15 Ex2 • In book Area of a Triangle • Using the law of sines, we can find the area K of a triangle K = 12 bcsin A = 12 absinC = 12 acsin B Ex6 • A university landscaping architecture department is designing a garden for a triangular area in a dormitory complex. Two sides of the garden, formed by the sidewalks in front of buildings A and B, measure 172 ft and 186 ft respectively, and together form a 53 degree angle. The third side of the garden measures 160 ft. Find the area of the garden to the nearest square foot. Closure • Find the area of the triangle ABC given C = 75.16 degrees, a = 1.5 m, b = 2.1 m • HW: p.608 #17-31 odds