Section 2.3 Sine Law © Copyright all rights reserved to Homework depot: www.BCMath.ca.

Slides:

Advertisements

Similar presentations

Section 5-6 The Law of Sines.

Advertisements

Law of Cosines Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 An oblique triangle is a triangle that has no right.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 2-1 Solving Right Triangles 2.4 Significant Digits ▪ Solving Triangles ▪ Angles of Elevation.

Laws of Sines and Cosines

Laws of Sines and Cosines Sections 6.1 and 6.2. Objectives Apply the law of sines to determine the lengths of side and measures of angle of a triangle.

Unit 5 Day 5: Law of Sines and the Ambiguous Case

7/3/ : The Law of Sines Expectation: G1.3.2: Know and use the Law of Sines and the Law of Cosines and use them to solve problems. Find the area.

TODAY IN ALGEBRA 2.0…  Learning Target : You will solve triangles that have NO RIGHT ANGLE using LAW OF COSINES.  Independent Practice.

Trigonometry Law of Sines Section 6.1 Review Solve for all missing angles and sides: a 3 5 B A.

The Law of Sines! Homework: Lesson 12.3/1-10, 12-14, 19, 20

Topic 1 Pythagorean Theorem and SOH CAH TOA Unit 3 Topic 1.

6.1 Law of Sines +Be able to apply law of sines to find missing sides and angles +Be able to determine ambiguous cases.

Slide Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Area of ANY Triangle B a C c b A If you know C, a and b

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

2-24 Honors Geometry Warm-up

Oblique Triangles Part I Learning Goal: I can solve for a missing side or angle in a non-right triangle using sine law.

Digital Lesson Law of Sines.

The Law of Sines Section 6.1 Mr. Thompson. 2 An oblique triangle is a triangle that has no right angles. Definition: Oblique Triangles To solve an oblique.

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?

Involving right triangles

Advanced Precalculus Notes 7.2 continued: Law of Sines (The Ambiguous Case) The Ambiguous Case: The reason there are two possible answers to 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.

Chapter 6.  Use the law of sines to solve triangles.

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.

Section Law of Sines and Area SAS Area 1-90 Since SAS determines a triangle, it should be possible to find its area given the 2 sides and the angle.

Chapter 6 Additional Topics in Trigonometry. 6.1 The Law of Sines Objectives:  Use Law of Sines to solve oblique triangles (AAS or ASA).  Use Law of.

6.1 Law of Sines.

Section 9.1 Applications Involving Right Triangles.

Chapter 6 Investigating Non-Right Triangles as Models for Problems: 6.4 Proving and Using the Sine Law.

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.

Law of Cosines Digital Lesson. Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 2 An oblique triangle is a triangle that has no right.

Math 20-1 Chapter 1 Sequences and Series 2.3B The Ambiguous Case of the Sine Law The Sine Law State the formula for the Law of Sines. What specific.

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

Digital Lesson Law of Sines.

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.

The Law of SINES.

1) Solve the triangle. Students,

Triangle Starters Pythagoras A | Answers Pythagoras B | B Answers

Find the missing parts of each triangle.

2) State the LAW OF COSINES.

Warm Up Chapter 3 Solve and graph on a number line: −

Chapter 2 - Trigonometry

Section 6.1 The Law of Sines

The Law of SINES.

2a Basic Trigonometric Functions Sine, Cosine, and tangent

Do Now If the legs of the right triangle are 4 and 5 find the hypotenuse and all the angles.

Section 3.4 Slopes of Parallel and Perpendicular Lines

Section 2.4 Cosine Law © Copyright all rights reserved to Homework depot:

Law of Sines and Cosines

Chapter 2 - Trigonometry

The Law of SINES.

Section 3.4 Sine Law and Cosine Law

Law of Sines and Cosines

The Law of SINES.

Section 6.5 Law of Cosines Objectives:

NOTES LAW OF SINES.

8-6 Using the Law of Sines Objectives:

The Law of SINES.

The Law of SINES.

8-5 Using the Law of Sines Objectives:

The Law of SINES.

Digital Lesson Law of Cosines.

The Law of SINES.

The Law of SINES.

Section 6.1 The Law of Sines

Law of Cosines Ref page 417.

Presentation transcript:

Section 2.3 Sine Law © Copyright all rights reserved to Homework depot: www.BCMath.ca

I) Sine Law The Sine Law is for solving triangles that are not R.T. Name each side with the opposite angle There are 3 separate equations The Sine Law can only be used when you are given one of the angles with its opposite side © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: A triangle ABC has side a = 12 cm, angle A = 60°, and angle C = 45°. Solve for side c.

Practice: Find the value of “x” Indicate the sides and angles Formula Cross Multiply and Solve for “X” © Copyright all rights reserved to Homework depot: www.BCMath.ca

II) Finding Missing Angles To find the angle, you need to use inverse sine If the angle is obtuse, you need to find the angle in Quadrant #2 Ex: Find the value of “θ” to the nearest degree Indicate the sides and angles Formula © Copyright all rights reserved to Homework depot: www.BCMath.ca

Example 2: A triangle has side a = 11 inches, angle A = 40°, and side c = 8 inches. Solve for angle C.

Practice: Find θ to the nearest degree Formula Formula Angle “B” is an OBTUSE angle, So it must be in Quadrant #2!! Angle “B” is an OBTUSE angle, So it must be in Quadrant #2!! © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: The angle of elevation to the top of the tower is 43° Ex: The angle of elevation to the top of the tower is 43°. If you travels 100m closer, the angle is 75°. How tall is the tower? Assume the person is about 1.5m tall. Make a Triangle and Gather Info Find the Hypotenuse of the triangle Use the Hypotenuse to find the opposite side Height of the Tower © Copyright all rights reserved to Homework depot: www.BCMath.ca

Example 7: At noon, two tracking stations on Earth , station A is 20 km west of station B, measure a rocket that was launched from a weather satellite. From station A the angle of elevation is 41° and from station B the angle of elevation was 75°. Find the height of the rocket above the earth. 9

Practice: A ship leaves Batumi on a bearing 300 and sails 860km Practice: A ship leaves Batumi on a bearing 300 and sails 860km. They then change direction on a bearing of 222 and sail for 580km and reached Istanbul. How far is Batumi from Istanbul? Turkey © Copyright all rights reserved to Homework depot: www.BCMath.ca

Proof For the Sine Law If we use another altitude for angle A, we can solve for the other part of the sine law © Copyright all rights reserved to Homework depot: www.BCMath.ca

HW: Assignment 2.3