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

Slides:

Advertisements

Similar presentations

The Law of Cosines February 25, 2010.

Advertisements

H.Melikian/ The Sines Law Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ 1.Determining if the Law of Sines Can Be Used to.

 Think back to geometry. Write down the ways to prove that two triangles are congruent.

Chapter 6 – Trigonometric Functions: Right Triangle Approach

Math III Accelerated Chapter 13 Trigonometric Ratios and Functions 1.

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.

19. Law of Sines. Introduction In this section, we will solve (find all the sides and angles of) oblique triangles – triangles that have no right angles.

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 6 Applications of Trigonometric Functions.

Copyright © 2009 Pearson Education, Inc. CHAPTER 8: Applications of Trigonometry 8.1The Law of Sines 8.2The Law of Cosines 8.3Complex Numbers: Trigonometric.

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

2-24 Honors Geometry Warm-up

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.

Law of Sines & Law of Cosines

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

9.5 Apply the Law of Sines When can the law of sines be used to solve a triangle? How is the SSA case different from the AAS and ASA cases?

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).

14. Law of Sines The Ambiguous Case (SSA). Yesterday we saw that two angles and one side determine a unique triangle. However, if two sides and one opposite.

Ambiguous Law of Sines Compute b sin A, then compare to a No solution One Solution Two Solutions One Solution Compute side a to side b No solution One.

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.

EXAMPLE 2 Solve the SSA case with one solution Solve ABC with A = 115°, a = 20, and b = 11. SOLUTION First make a sketch. Because A is obtuse and the side.

Class Work Let’s start with some review!! 1.Solve for x. x 7 42 

6.1 Law of Sines If ABC is an oblique triangle with sides a, b, and c, then A B C c b a.

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 9.3 Evaluate Trigonometric Functions of Any Angle Warm-Up Standard Accessed: Students.

Warm-Up 10/15 1. H PSAT Tomorrow 10/16, you will need to bring your own calculator.

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

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.

Trigonometry Ratios.

The Law of Sines Day 1: Areas and AAS

Law of Sines & Law of Cosine. Law of Sines The ratio of the Sine of one angle and the length of the side opposite is equivalent to the ratio of the Sine.

TRIGONOMETRY Lesson 2: Solving Right Triangles. Todays Objectives Students will be able to develop and apply the primary trigonometric ratios (sine, cosine,

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.

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° =

Sullivan Algebra and Trigonometry: Section 9.2 Objectives of this Section Solve SAA or ASA Triangles Solve SSA Triangles Solve Applied Problems.

Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Lesson 9.2 Define General Angles and Use Radian Measure Warm-Up Standard Accessed: Students.

Law of Sines Use it when you are given Angle-Angle-Side (AAS) Angle-Side-Angle (ASA) Side-Side-Angle (SSA)

Law of Sines Objective: To solve triangles that are not right triangles.

8-5 The Law of Sines Objective: To apply the Law of Sines Essential Understanding : If you know the measures of two angles and the length of a side(AAS.

CHAPTER 5 LESSON 4 The Law of Sines VOCABULARY  None.

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.

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.

5.7 The Ambiguous Case for the Law of Sines

Objective: Use the law of sine. (SSA)

Unit 6: Trigonometry Lesson: Law of coSines.

6.1 Law of Sines Objectives:

Lesson 37 continued Get out your notes from yesterday.

Warm UP Find the area of an oblique triangle ABC. Where angle A = 32degrees Side b= 19, and side c = 32.

Objective: To apply the Law of Sines

LAW of SINES Standard Cases.

6-3: Law of Cosines

Lesson 34 - Review of the Sine Law

Re:view Use the Law of Sines to solve: Solve ABC

Find the missing parts of each triangle.

Essential question: How do I solve oblique triangles?

Section 8.1 The 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.

Section 6.2 The Law of Cosines

5.5 Law of Sines.

8-6 Using the Law of Sines Objectives:

8-5 Using the Law of Sines Objectives:

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.

The Law of Sines.

When can we use the Sine Law?

Presentation transcript:

Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Lesson 9.5 Apply the Law of Sines Warm-Up Standard Accessed: Students will prove, apply, and model trigonometric functions and ratios.

Warm-Up Solve Δ XYZ.

Solve Δ ABC.

Vocabulary Can be used to solve triangles with no right angle, when two angles and the length of any side are known (AAS or ASA cases), or when the lengths of two sides and an angle opposite one of the two sides are known, (SSA).

Essential Understandings When can the Law of sines be used to solve a triangle?  When two angles and the length of any side are known (AAS or ASA cases), or when the lengths of two sides and an angle opposite one of the two sides are known, (SSA). The law of sines is used to solve triangles with no right angle.

Solve a triangle for the AAS or ASA case EXAMPLE 1 SOLUTION 3. Write the Law of Sine proportion 1. Draw a picture 4. Write the Law of Sine proportion

Solve a triangle for the AAS or ASA case EXAMPLE 1 When you are given the measures of two angles and one side of a triangle, why does it not matter whether the given side is the one included between the two angles? It does not matter since you are given the measures of any two angles, you can always find the third angle measure. Key Question

Essential Understandings What are the possible triangles for the SSA case?

Solve the SSA case with one solution EXAMPLE 2 SOLUTION 3. Write the Law of Sine proportion 2. Draw a picture 5. Write the Law of Sine proportion

Examine the SSA case with no solution EXAMPLE 3 SOLUTION 2. Draw a picture What will happen if you try to solve the triangle by applying the law of sines and using your calculator? Write the Law of Sine proportion

Solve the SSA case with two solutions EXAMPLE 4 SOLUTION 3. Write the Law of Sine proportion 2. Draw a picture 5. Write the Law of Sine proportion

Vocabulary

Write and Solve a real – Use trig to find area of triangle EXAMPLE 4 KIS Vegetable Garden Esther and Frederick are setting up a triangular vegetable garden at KIS. They lay off lengths of 15ft and 11ft for two sides of the garden with a 62° angle between these two sides, what will be the area of the garden? 1. Draw a picture SOLUTION

Lesson 9.5 Homework: Practice B Practice C “Honors”