Solve the oblique triangle with the following measurements:

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Presentation transcript:

Solve the oblique triangle with the following measurements: Warm up: Solve the oblique triangle with the following measurements: A = 80, c = 10, a = 7 HW: pg.527(1 – 10, 13 – 14, 17 – 22) Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

6.2 Law of Cosines Objective: Solve oblique triangles using the law of cosines. Murphy's Law: Anything that can possibly go wrong, will go wrong (at the worst possible moment). Cole's Law ?? Finely chopped cabbage

Two angles and any side (AAS or ASA) Recall: The following cases are considered when solving oblique triangles. Two angles and any side (AAS or ASA) A C c A B c 2. Two sides and an angle opposite one of them (SSA) C c a No solution 1 solution 2 solutions Possible ambiguity 3. Three sides (SSS) a c b c a B 4. Two sides and their included angle (SAS) The first two cases we use the Law of Sines! Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Solving an SAS or SSS Triangle Why would the Law of Sines not work for an SAS or SSS triangle? No side opposite from any angle to get the ratio 15 26° 12.5 17 10 15

Deriving the Law of Cosines b h a Write an equation using the Pythagorean theorem for the shaded triangle. k c - k A B c

The last two cases (SSS and SAS) can be solved using the Law of Cosines. Standard Form Alternative Form Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Find the three angles of the triangle. C Example: Find the three angles of the triangle. C B A 8 6 12 117.3 26.4 36.3 Find the angle opposite the longest side first. Law of Sines: Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Example: C B A Solve the triangle. Law of Cosines: Law of Sines: 67.8 6.2 75 9.5 Solve the triangle. 67.8 9.9 Law of Cosines: 37.2 Law of Sines: Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Definition: Heron’s Area Formula Given any triangle with sides of lengths a, b, and c, the area of the triangle is given by 5 10 8 Example: Find the area of the triangle. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Definition: Heron’s Area Formula

Solve the oblique triangle with the following measurements: Sneedlegrit: Solve the oblique triangle with the following measurements: a = 7, b = 8, c = 9 HW: pg.527(1 – 10, 13 – 14, 17 – 22) Copyright © by Houghton Mifflin Company, Inc. All rights reserved.