NOTES Law of Cosines.

Slides:

Advertisements

Similar presentations

The Law of Cosines February 25, 2010.

Advertisements

Chapter 6 – Trigonometric Functions: Right Triangle Approach

Starter a 6 c A 49° 96° 1.Use the Law of Sines to calculate side c of the triangle. 2.Now find the Area of a Triangle.

The Law of SINES.

Law of Cosines Lesson Who's Law Is It, Anyway?  Murphy's Law: Anything that can possibly go wrong, will go wrong (at the worst possible moment).

Ambiguous Case Triangles

Laws of Sines. Introduction  In the last module we studied techniques for solving RIGHT triangles.  In this section and the next, you will solve OBLIQUE.

Copyright © 2011 Pearson, Inc. 5.5 Law of Sines. Copyright © 2011 Pearson, Inc. Slide What you’ll learn about Deriving the Law of Sines Solving.

Law of Sines. Triangles Review Can the following side lengths be the side lengths of a triangle?

13.4 L AW OF S INES 13.5 L AW OF COSINES Algebra II w/ trig.

Chapter 5: Trigonometric Functions Lesson: Ambiguous Case in Solving Triangles Mrs. Parziale.

Triangle Warm-up Can the following side lengths be the side lengths of a triangle?

6.2 The Law of Cosines.

Section 6.1. Law of Sines Use the Law of Sines when given: Angle-Angle-Side (AAS) Angle-Side-Angle (ASA) Side-Side-Angle (SSA)

5.5 Law of Sines. I. Law of Sines In any triangle with opposite sides a, b, and c: AB C b c a The Law of Sines is used to solve any triangle where you.

6.1 Law of Sines. Introduction Objective: Solve oblique triangles To solve: you must know the length of one side and the measures of any two other parts.

Trigonometry Section 6.1 Law of Sines. For a triangle, we will label the angles with capital letters A, B, C, and the sides with lowercase a, b, c where.

Notes Over 8.1 Solving Oblique Triangles To solve an oblique triangle, you need to be given one side, and at least two other parts (sides or angles).

Math /7.2 – The Law of Sines 1. Q: We know how to solve right triangles using trig, but how can we use trig to solve any triangle? A: The Law of.

Lesson 6.5 Law of Cosines. Solving a Triangle using Law of Sines 2 The Law of Sines was good for: ASA- two angles and the included side AAS- two angles.

Section 4.2 – The Law of Sines. If none of the angles of a triangle is a right angle, the triangle is called oblique. An oblique triangle has either three.

Toothpicks and PowerPoint Ambiguous Case of the Law of Sines Pam Burke Potosi High School #1 Trojan Drive Potosi, MO

Law of Sines AAS ONE SOLUTION SSA AMBIGUOUS CASE ASA ONE SOLUTION Domain error NO SOLUTION Second angle option violates triangle angle-sum theorem ONE.

Law of Cosines HOMEWORK: Lesson 12.4/ Who's Law Is It, Anyway?  Murphy's Law: Anything that can possibly go wrong, will go wrong (at the worst.

LAW OF COSINES. SOLVING AN SAS TRIANGLE The Law of Sines was good for ASA- two angles and the included side AAS- two angles and any side SSA- two sides.

Sine Law Homework Questions??? Pg. 25 # 3, 5, 7, 9.

The Law of SINES.

Section T.5 – Solving Triangles

Oblique Triangles.

If none of the angles of a triangle is a right angle, the triangle is called oblique. All angles are acute Two acute angles, one obtuse angle.

WARM UP Use a calculator to find the approximate value. Express your answer in degrees. (Hint: check the mode of your calculator)

Law of sines 6-1.

Objective: Use the law of sine. (SSA)

5.6 The sine law Watch this!! Ambiguous Case

Unit 6: Trigonometry Lesson: Law of coSines.

6.1 Law of Sines Objectives:

6-3: Law of Cosines

Ambiguous Case Triangles

The Law of Sines.

Law of Cosine Chapter 8.3.

Essential question: How do I solve oblique triangles?

Law of Sines What You will learn:

50 a 28.1o Warm-up: Find the altitude of the triangle.

Law of Cosines Lesson 4.2.

8-5 The Law of Sines Geometry.

5.5 Law of Sines.

15. Law of Cosines.

Law of Cosines Lesson 4.2.

Law of Sines and Cosines

Law of Sines Notes Over If ABC is a triangle with sides a, b, c, then according to the law of sines, or.

Solve the oblique triangle with the following measurements:

Law of Sines AAS ONE SOLUTION SSA AMBIGUOUS CASE ASA ONE SOLUTION

Law of Cosines.

Law of Cosines.

Section 6.2 The Law of Cosines

5.5 Law of Sines.

Law of Sines and Law of Cosines

Law of Sines. Law of Sines Non Right Triangles How is a triangle classified if none of the angles are 90? Oblique Labeling Oblique Triangles To solve.

Law of Cosines.

LT: I can use the Law of Sines and the Law of Cosines to find missing measurements on a triangle. Warm-Up Find the missing information.

7.1, 7.2, 7.3 Law of Sines and Law of Cosines

Ambiguous Case Triangles

7.2 The Law of Sines.

Law of Cosines Lesson 1.6.

Law of Sines and Law of Cosines

Law of Sines (Lesson 5-5) The Law of Sines is an extended proportion. Each ratio in the proportion is the ratio of an angle of a triangle to the length.

The Law of Sines.

When can we use the Sine Law?

Presentation transcript:

NOTES Law of Cosines

Who's Law Is It, Anyway? Murphy's Law: Cole's Law ?? Anything that can possibly go wrong, will go wrong (at the worst possible moment). Cole's Law ?? Finely chopped cabbage

Solving an SAS Triangle The Law of Sines was good for ASA - two angles and the included side AAS - two angles and any side SSA - two sides and an opposite angle (being aware of possible ambiguity) Why would the Law of Sines not work for an SAS triangle? 15 No side opposite from any angle to get the ratio 26° 12.5

Law of Cosines

Applying the Cosine Law Now use it to solve the triangle we started with Label sides and angles Side c first C 15 26° 12.5 A B c

Applying the Cosine Law Now calculate the angles use and solve for B C 15 26° 12.5 A B c = 6.65

Applying the Cosine Law The remaining angle determined by subtraction 180 – 93.75 – 26 = 60.25 C 15 26° 12.5 A B c = 6.65 Experiment with Cosine Law Spreadsheet