Section 1.3.2 Law of Cosines. Law of Cosines: SSS or SAS Triangles 1-106 Use the diagram to complete the following problems, given triangle ABC is acute.

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Presentation transcript:

Section Law of Cosines

Law of Cosines: SSS or SAS Triangles Use the diagram to complete the following problems, given triangle ABC is acute. B AC a) Find e in terms of side b and d. b) Use the Pythagorean theorem, find an equation that relates c, h, & e. Solve the equation for h². c) Use the Pythagorean theorem, find an equation that relates a, h, & d. Solve the equation for h².

Law of Cosines: SSS or SAS Triangles B A C d) Write a single equation from parts b and c. Rewrite the eq so it begins with c². e) Replace e in the equation with results from part a. Expand and simplify. f) Use the lengths a, b, & c only in the formula. Find an expression that uses d, a, and angle C. Solve the equation for d. g) Combine the results from parts d & e.

The Law of Cosines in 3 parts: Do you see a pattern?

Example: In  SUN, s = 6, u = 12 and n = 8 cm. Solve  SUN. S N U

Lesson Close The Law of Cosines is used to solve triangles when: Two sides and an included angle are known Three sides are known

Assignment Pg 42 #1-107 TO 1-122