Toothpicks and PowerPoint Ambiguous Case of the Law of Sines Pam Burke Potosi High School #1 Trojan Drive Potosi, MO 63664 573-438-2156

Slides:

Advertisements

Similar presentations

The Ambiguous Case of the Law of Sines

Advertisements

(application of the Ambiguous Case

The Law of Cosines February 25, 2010.

Chapter 6 Trigonometry- Part 3. Aim #6.1:How do we apply the Law of Sines? An oblique triangle is one that does not contain a right angle.

Chapter 6 – Trigonometric Functions: Right Triangle Approach

Math III Accelerated Chapter 13 Trigonometric Ratios and Functions 1.

Module 8 Lesson 5 Oblique Triangles Florben G. Mendoza.

Section SOLVING OBLIQUE TRIANGLES

Math 112 Elementary Functions Section 2 The Law of Cosines Chapter 7 – Applications of Trigonometry.

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.

Assignment Trig Ratios III Worksheets (Online) Challenge Problem: Find a formula for the area of a triangle given a, b, and.

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).

Triangles- The Ambiguous Case Lily Yang Solving Triangles If you are given: Side-Side-Side (SSS) or Side-Angle-Side (SAS), use the Law of Cosines.

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.

Lesson 6.1 Law of Sines. Draw any altitude from a vertex and label it k. Set up equivalent trig equations not involving k, using the fact that k is equal.

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?

1 Law of Cosines Digital Lesson. 2 Law of Cosines.

6.2 The Law of Cosines.

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.

Section 5-5 Law of Sines. Section 5-5 solving non-right triangles Law of Sines solving triangles AAS or ASA solving triangles SSA Applications.

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.

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.

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).

Sec. 5.5 Law of sines.

7.1 The Law of Sines 56 46° 63° A B C. 7.1 The Law of Sines 14 64° 82° A B C.

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.

Chapter 8 Section 8.2 Law of Cosines. In any triangle (not necessarily a right triangle) the square of the length of one side of the triangle is equal.

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.

Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Lesson 9.5 Apply the Law of Sines Warm-Up Standard Accessed: Students will prove, apply,

Lesson 6.1- Law of Sines Provided by Vivian Skumpija and Amy Gimpel.

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.

Section Take a note: Up until now, our work with triangles has involved right triangles, And for that we use the Pythagorean Theorem. But there.

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.

What you’ll learn Use the Law of Sines to solve oblique triangles. Use the Law of Sines to solve, if possible, the triangle or triangles in the ambiguous.

1.Name the different types of triangles 2.What is the angle sum of a triangle rule? 3.What is Pythagorean Theorem and when can we use it? 4.What do you.

Section T.5 – Solving 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.

9.1 Law of Sines.

Objective: Use the law of sine. (SSA)

Unit 6: Trigonometry Lesson: Law of coSines.

The Law of Sines.

Law of Cosine Chapter 8.3.

Law of Sines What You will learn:

Law of Cosines Lesson 4.2.

Solving OBLIQUE triangles (ssa)

5.5 Law of Sines.

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.

NOTES 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.

The Law of Sines.

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

7.2 The Law of Sines.

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.

6.1 Laws of Sines.

The Law of Sines.

Section 6.1 The Law of Sines

Presentation transcript:

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

To solve a right triangle, you can use the Pythagorean Theorem and/or basic trig ratios. C A B a b c

In an oblique triangle (one in which there are no right angles) neither of those methods will work. Solving an oblique triangle requires using either the Law of Sines or the Law of Cosines, depending on which information you are given.

In this lesson we are going to use the Law of Sines.

The Law of Sines can be used when you are given two angles and one side of an oblique triangle (ASA or AAS).

Here is an example. You are given two angles and one side of a triangle. Find the measures of the other angle and the other two sides. A B C a b c A = 65º a = 28 B = 32º b = ? C = ? c = ?

A B C a b c A = 65º a = 28 B = 32º b = ? C = ? c = ? C = 180º - (A + B) = 180º - ( ) = 180º - 97º = 83º

A B C a b c A = 65º a = 28 B = 32º b = ? C = 83º c = ?

A B C a b c A = 65º a = 28 B = 32º b ≈ 16.4 C = 83º c = ?

A = 65º a = 28 B = 32º b ≈ 16.4 C = 83º c ≈ 30.7 A B C a b c Now you have solved the triangle; you know the measures of all three sides and all three angles.

The Law of Sines can also be used to solve an oblique triangle when you are given two sides and the angle opposite one of the sides (SSA).

b a A Suppose you are given the measures shown below for two sides and an angle of an oblique triangle.

b A a The pieces could be put together to form this triangle.

b A a But they could also be put together to form this triangle.

Since SSA does not always define a unique triangle, this is called the Ambiguous Case of the Law of Sines. b A a b A a