Copyright © 2011 Pearson, Inc. 5.5 Law of Sines Goal: Solve triangles that have no solution, one solution, or two solutions.

Slides:



Advertisements
Similar presentations
Copyright © 2011 Pearson, Inc. 5.6 Law of Cosines Goal: Apply the Law of Cosines.
Advertisements

Aim: What is the Law of Sine? Do Now: In ∆ABC, AC = b, BC = a, and the height is (h). Find: 1. sin A 2. sin B A D B C HW: p.567 # 6,8,12,19,20,21,22,23.
Chapter 6 Additional Topics in Trigonometry Copyright © 2014, 2010, 2007 Pearson Education, Inc The Law of Sines.
Chapter 6 – Trigonometric Functions: Right Triangle Approach
Module 8 Lesson 5 Oblique Triangles Florben G. Mendoza.
Section SOLVING OBLIQUE TRIANGLES
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 8.2 The Law of Sines.
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 © 2009 Pearson Education, Inc. CHAPTER 8: Applications of Trigonometry 8.1The Law of Sines 8.2The Law of Cosines 8.3Complex Numbers: Trigonometric.
The Law of Sines. Quick Review Quick Review Solutions.
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.
13.4 L AW OF S INES 13.5 L AW OF COSINES Algebra II w/ trig.
Chapter 6 Additional Topics: Triangles and Vectors 6.1 Law of Sines 6.2 Law of Cosines 6.3 Areas of Triangles 6.4 Vectors 6.5 The Dot Product.
Triangle Warm-up Can the following side lengths be the side lengths of a triangle?
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.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5- 1 Homework, Page 468 Use a sum or difference identity to find an.
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.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5- 1.
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.
7.1 The Law of Sines Congruence Axioms
9-3 L AW OF S INES. L AW OF S INES A B Given an oblique triangle (no right angle) we can draw in the altitude from vertex B Label the altitude k and find.
The Law of Sines Day 1: Areas and AAS
EXAMPLE 1 Solve a triangle for the AAS or ASA case Solve ABC with C = 107°, B = 25°, and b = 15. SOLUTION First find the angle: A = 180° – 107° – 25° =
Section 8.1: Right Triangle Trigonometry: Applications and Section 8.2: Law of Sines Copyright © 2013 Pearson Education, Inc. All rights reserved.
Law of Cosines. SAS Area Formula: A b c Heron’s SSS Area Formula: b c a.
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.
Make it a great day!! The choice is yours!! Complete the Do Now.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
The Law of Sines & Cosines
Advanced Geometry Trigonometry Lesson 5 The Law of Cosines.
Chapter 4 Laws of Sines and Cosines; Vectors 4.1 The Law of Sines 1
The Law of SINES.
Section T.5 – Solving Triangles
Digital Lesson Law of Sines.
Demana, Waits, Foley, Kennedy
5.6 Law of Cosines.
WARM UP Use a calculator to find the approximate value. Express your answer in degrees. (Hint: check the mode of your calculator)
Warm Up Ship A is 72 miles from a lighthouse that is on the shore. The ships bearing from the lighthouse is S 15° E. Ship B is 81 miles from the same lighthouse.
Objective: Use the law of sine. (SSA)
Section 8.2 The Law of Sines
Section 8.2 The Law of Cosines
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
The Law of Sines.
Law of Cosine Chapter 8.3.
Law of Sines What You will learn:
Section 8.1 The Law of Sines
50 a 28.1o Warm-up: Find the altitude of the triangle.
Solving OBLIQUE triangles (ssa)
5.5 Law of Sines.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 6.1.
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
Section 9.2 The Law of Sines
Law of Cosines.
Law of Cosines.
Law of Cosines C a b A B c.
5.5 Law of Sines.
Section 9.2 The Law of Sines
Geometry Section 7.7.
Law of Sines and Law of Cosines
Chapter 9 Law of Cosines and Law of Sines
When can we use the Sine Law?
Presentation transcript:

Copyright © 2011 Pearson, Inc. 5.5 Law of Sines Goal: Solve triangles that have no solution, one solution, or two solutions.

Copyright © 2011 Pearson, Inc. Slide What you’ll learn about Deriving the Law of Sines Solving Triangles (AAS, ASA) The Ambiguous Case (SSA) Applications … and why The Law of Sines is a powerful extension of the triangle congruence theorems of Euclidean geometry.

Copyright © 2011 Pearson, Inc. Slide Law of Sines

Copyright © 2011 Pearson, Inc. When should you use the… Law of Cosines? Law of Sines?

Copyright © 2011 Pearson, Inc. Find AB.

Copyright © 2011 Pearson, Inc. Find BC.

Copyright © 2011 Pearson, Inc. Find all possible values of angle C to the nearest degree.

Copyright © 2011 Pearson, Inc. How did you draw your triangle?

Copyright © 2011 Pearson, Inc.

Find the height of the tree to the nearest foot. Slide

Copyright © 2011 Pearson, Inc. Locating a Fire Slide