Date: 6.2(b) Notes: Derive the Law of Cosines Lesson Objective: Derive and use the Law of Cosines to solve oblique triangles. CCSS: F-TF Extend the domain of tri­go­no­me­tric functions using the unit circle. You will need: calculator Real-World App: What is the area the airplanes covered? This is Jeopardy!!!: These were the angles of the airplanes for 6.2(a) Notes Lesson 2.

Lesson 1: The Law of Cosines for SSS Law of Cosines: Use this to find 3 rd side when given SAS or an angle for SSS. C a 2 = b 2 + c 2 – 2bc cos A b a (b – c) 2 Included angle A c B Derived from the Pythagorean Theorem

Lesson 1: The Law of Cosines for SSS Solve triangle ABC if a = 8, b = 10, and c = 5. Round to the nearest tenth.

Lesson 2: Area Using Heron’s Formula How can we find the area of this triangle? What did we need to find the area of an oblique triangle using trig?

Lesson 2: Area Using Heron’s Formula Heron’s Formula for the Area of a Triangle: Derived from the half-angle formula and the Law of Cosines; used on SSS oblique Δ

Lesson 2: Area Using Heron’s Formula Find the area of the triangle with a = 6 m, b = 16 m, and c = 18 m. Round to the tenth

Lesson 3: Real-World App Using Heron’s Two airplanes leave an airport at the same time on different runways. One flies directly north at 400 miles per hour. The other plane flies on a bearing of N75°E at 350 miles per hour. What area did the airplanes cover? Plane 1 distance: d 1 = Plane 2 distance: d 2 = Distance between airplanes =

6.2(b): Do I Get It? Yes or No 1.Solve triangle ABC if a = 6, b = 9, and c = 4. Round to the nearest tenth. 2.Find the area of the triangle with a = 12 yds, b = 16 yds, and c = 24 yds. Round to the nearest tenth. 3.Two airplanes leave an airport at the same time on different runways. One flies on a bear­ing of N66°W at 325 mi per hr. The other flies on a bearing of S26°W at 300 mi per hr. What area did the airplanes cover?

Answers: 1.B = 127°, A = 32°, C = 21° 2.Area = 85 yds 2