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Exploring Triangle Area Formulas in Mathematics

Learn about solving triangles using Law of Cosines and the area of triangles formula in this homework assignment. Understand when to apply Law of Sines and Cosines based on given information.

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Exploring Triangle Area Formulas in Mathematics

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  1. Pg. 435 Homework • Pg. 443 #1 – 10 all, 13 – 18 all • #3 ɣ = 110°, a = 12.86, c = 18.79 #4 No triangle possible • #5 α = 90°, ɣ = 60°, c = 10.39 • #6 b = 4.61, c = 4.84, ɣ = 68° • #7 a = 3.88, c = 6.61, ɣ = 68° • #8 α = 41.62°, ɣ = 53.38°, c = 4.83 • #10 α = 29.51°, ɣ = 112.49°, c = 30.01 • #12 α = 49.51°, ɣ = 14.49°, c = 3.62 • #13 No triangle possible #14 No triangle possible • #15 α = 22.06°, ɣ = 5.94°, c = 2.20 • #18 a)54.60 ft b) 51.93 ft apart • #21 0.72 miles high

  2. 8.2 Law of Cosines Definition Law of Cosines For any triangle ABC, labeled in the usual way Solve triangle ABC ifa = 5, b = 3, ɣ= 35°. Solve triangle ABC ifa = 9, b = 7, c = 5. • Law of Sines is best for when you have two angles and one side or when two sides and a non-included angle are given. • Law of Cosines is best when you have two sides and the included angle (Law of Sines does not apply here!)

  3. 8.2 Law of Cosines Solving an Oblique Triangle Area of Triangles Let ABC be a triangle labeled in the usual way. Then the area A of the triangle is given by:

  4. 8.2 Law of Cosines Heron’s Area Formula Examples: Use the best method to find the area. Find the area of triangle ABC if a = 8, b = 5, ɣ = 52°. Find the area of triangle ABC if a = 9, b = 7, c = 5. • Let ABC be a triangle labeled in the usual way. Then the area A of the triangle is given by:where is one half the perimeter, or the semiperimeter.

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