Splash Screen. Then/Now You used trigonometric ratios to solve right triangles. Use the Law of Sines to solve triangles. Use the Law of Cosines to solve.

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Presentation transcript:

Splash Screen

Then/Now You used trigonometric ratios to solve right triangles. Use the Law of Sines to solve triangles. Use the Law of Cosines to solve triangles.

Vocabulary Law of Sines Law of Cosines

Concept

Example 1 Law of Sines (AAS or ASA) Find p. Round to the nearest tenth. We are given measures of two angles and a nonincluded side, so use the Law of Sines to write a proportion.

Example 1 Law of Sines (AAS or ASA) Law of Sines Use a calculator. Divide each side by sin Cross Products Property Answer: p ≈ 4.8

Example 1 A.4.6 B.29.9 C.7.8 D.8.5 Find c to the nearest tenth.

Example 2 Law of Sines (ASA) Find x. Round to the nearest tenth. 6 x 57 °

Example 2 A.8 B.10 C.12 D.14 Find x. Round to the nearest degree. 43 ° x

Concept

Example 3 Law of Cosines (SAS) Find x. Round to the nearest tenth. Use the Law of Cosines since the measures of two sides and the included angle are known.

Example 3 Law of Cosines (SAS) Answer: x ≈ 18.9 Simplify. Take the square root of each side. Law of Cosines Use a calculator.

Example 3 A.25.1 B.44.5 C.22.7 D.21.1 Find r if s = 15, t = 32, and m  R = 40. Round to the nearest tenth.

Example 4 Law of Cosines (SSS) Find m  L. Round to the nearest degree. Law of Cosines Simplify.

Example 4 Law of Cosines (SSS) Answer: m  L ≈ 49 Solve for L. Use a calculator. Subtract 754 from each side. Divide each side by –270.

Example 4 A.44° B.51° C.56° D.69° Find m  P. Round to the nearest degree.

Homework: Pg. 592 #’s 1 - 6