Pre calculus Problem of the Day Homework p. p. 635 1-15 odds, 33-37 odds Find the area of a triangle with the given dimensions. r = 15 in s = 13 in t.

Slides:



Advertisements
Similar presentations
Chapter 6 Additional Topics in Trigonometry Copyright © 2014, 2010, 2007 Pearson Education, Inc The Law of Sines.
Advertisements

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.
 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.
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.
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. When Do I use Law of Sines vs. Law of Cosine ? Two sides One opposite angle given Angle opposite side Two angles One opposite side given.
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.
LAW OF SINES: THE AMBIGUOUS CASE. Review Identify if the given oblique triangle can be solved using the Law of Sines or the Law of Cosines 1. X = 21 0,
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?
6.1 Laws of Sines. The Laws of Sine can be used with Oblique triangle Oblique triangle is a triangle that contains no right angle.
LAW OF SINES: THE AMBIGUOUS CASE MENTAL DRILL Identify if the given oblique triangle can be solved using the Law of Sines or the Law of Cosines 1.
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.
Homework Questions. LOGS Warm-up Convert from log form to exponential form Convert from exponential form to log form Expand Condense.
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.
Section 9-3 The Law of Sines. Recall…  When there are several methods for solving a problem, a comparison of the solutions can lead to new and useful.
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.
7.1 The Law of Sines 56 46° 63° A B C. 7.1 The Law of Sines 14 64° 82° A B C.
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.
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 
1 Equations 7.3 The Law of Cosines 7.4 The Area of a Triangle Chapter 7.
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.
The Law of Sines Day 1: Areas and AAS
Law of Sines Section 6.1. So far we have learned how to solve for only one type of triangle Right Triangles Next, we are going to be solving oblique triangles.
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° =
Law of Sines Use it when you are given Angle-Angle-Side (AAS) Angle-Side-Angle (ASA) Side-Side-Angle (SSA)
Homework Questions. LOGS Warm-up Evaluating Logs.
6.4 Law Of Sines. The law of sines is used to solve oblique triangles; triangles with no right angles. We will use capital letters to denote angles of.
PreCalculus 6-1 Law of Sines. This lesson (and the next) is all about solving triangles that are NOT right triangles, these are called oblique triangles.
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.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Chapter 4 Laws of Sines and Cosines; Vectors 4.1 The Law of Sines 1
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.
5.7 The Ambiguous Case for the Law of Sines
9.1 Law of Sines.
Objective: Use the law of sine. (SSA)
Unit 6: Trigonometry Lesson: Law of coSines.
Warm-Up Solve the following triangle 14 61o *Homework Check*
6.1 Law of Sines Objectives:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
The Ambiguous Case (SSA)
The Law of SINES.
6-3: Law of Cosines
Essential question: How do I solve oblique triangles?
Law of Sines What You will learn:
1) State the LAW OF SINES. 2) Find a. Students,
Warm Up Chapter 3 Solve and graph on a number line: −
Solving OBLIQUE triangles (ssa)
Homework Questions.
Homework Questions.
The Law of SINES.
5.5 Law of Sines.
Homework Questions.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 1.5 Law of Sines.
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.
5.5 Law of Sines.
Section 6.5 Law of Cosines Objectives:
8-6 Using the Law of Sines Objectives:
8-5 Using the Law of Sines Objectives:
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.
Section 6.1 The Law of Sines
Presentation transcript:

Pre calculus Problem of the Day Homework p. p odds, odds Find the area of a triangle with the given dimensions. r = 15 in s = 13 in t = 20 in R = 30˚ 65 square inches

If you know two sides and the included angle on any triangle, the area of the triangle will be:

Using our three forms of the area of triangle ABC we have,

This relationship is called The Law of Sines and can be used to solve triangles that don’t have a right angle.

Pre calculus Problem of the Day Homework: p odds, odds Solve the following on the interval [0,360) degrees. sin x =.3508

Solve the triangle that has the following dimensions.

Law of Sines and the Ambiguous Case When given SSA for a triangle, there may be 0, 1, or 2 solutions for the given triangle.