Warm-up Determine the measure of the missing angle, theta in the obtuse triangle below. 2.7 3.0 46o.

Slides:

Advertisements

Similar presentations

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. X.

Advertisements

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

Chapter 6 – Trigonometric Functions: Right Triangle Approach

Section SOLVING OBLIQUE TRIANGLES

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

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,

Law of Sines & Law of Cosines

6.1 Law of Sines Objectives –Use the Law of Sines to solve oblique triangles –Use the Law of Sines to solve, is possible, the triangle or triangles in.

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?

The Ambiguous Case for the Law of Sines

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.

6.1 Law of Sines Objective To use Law of Sines to solve oblique triangles and to find the areas of oblique triangles.

Section 6.1. Law of Sines Use the Law of Sines when given: Angle-Angle-Side (AAS) Angle-Side-Angle (ASA) Side-Side-Angle (SSA)

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.

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).

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

Warm up A 5.2 m ladder leans against a wall. The bottom of the ladder is 1.9 m from the wall. What angle does the ladder make with the ground (to.

Law of Sines Day 2- The ambiguous case. Reminder Yesterday we talked in great detail of the 2/3 cases in which you can use law of sines: AAS ASA Today.

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.

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.

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.

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.

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

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.

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.

WARM UP Use a calculator to find the approximate value. Express your answer in degrees. (Hint: check the mode of your calculator)

5.7 The Ambiguous Case for the Law of Sines

Objective: Use the law of sine. (SSA)

5.6 The sine law Watch this!! Ambiguous Case

Warm-Up Solve the following triangle 14 61o *Homework Check*

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.

The Ambiguous Case (SSA)

The Law of SINES.

Find the missing parts of each triangle.

Law of Sines What You will learn:

50 a 28.1o Warm-up: Find the altitude of the triangle.

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

The Law of SINES.

The Laws of SINES and COSINES.

The Law of SINES.

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

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.

The Law of SINES.

The Law of SINES.

The Law of SINES.

5.5 Law of Sines.

NOTES LAW OF SINES.

The Law of SINES.

The Law of SINES.

The Law of SINES.

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.

The Law of SINES.

The Law of SINES.

Presentation transcript:

Warm-up Determine the measure of the missing angle, theta in the obtuse triangle below. 2.7 3.0 46o

Homework Issues??? (page 163 # 2, 3; page 170 # 5, 7, 10, 12 - 14)

The of the Sine Law

By definition, the word ambiguous means open to two or more interpretations. Such is the case for certain solutions when working with the  Law of Sines. If you are given two angles and a side opposite (ASA or AAS), the Law of Sines will nicely provide you with ONE solution for a missing side.  Unfortunately, the Law of Sines has a problem dealing with SSA. If you are given information about two sides and one angle which is not contained, with no diagram, there could be zero, one, or two possible triangles that could be drawn.

For Example: In triangle ABC, angle A = 30 degrees, b = 5 and a = 3. Determine the length of c.

How can we determine how many possible triangles there are based on a particular situation??? We can always start be determining the height of the triangle.

height of triangle C A B B'

a < b sinA, there is no solution a = b sinA, there is ONE solution So, if: a < b sinA, there is no solution a = b sinA, there is ONE solution a > b sinA, there are TWO solutions a > b, there is ONE triangle only. height of triangle Note: a is the side opposite the angle. C A B b a a<bsinA = no triangle a=bsinA = one rt < triangle a>bsinA = two possible triangles

http://jwilson. coe. uga. edu/EMT668/EMAT6680 http://jwilson.coe.uga.edu/EMT668/EMAT6680.2001/Mealor/EMAT%206700/law%20of%20sines/Law%20of%20Sines%20ambiguous%20case/lawofsinesambiguouscase.html

In triangle ABC, angle A = 47 degrees, b = 10 cm In triangle ABC, angle A = 47 degrees, b = 10 cm. Find possible values of side "a" that would result in .... a) no triangles b) 1 right triangle c) 2 triangles d) 1 obtuse triangle.

Textbook Questions: Pages 183 - 185 # 4, 5, 6, 7, 9, 11 *Due tomorrow!

In triangle ABC angle A = 50 degrees, side b = 14 cm and side a = 12 cm. Calculate the measures of angles B and C.

Example 1: In triangle ABC, <A = 42o, a = 7. 2cm and b = 8. 5cm Example 1: In triangle ABC, <A = 42o, a = 7.2cm and b = 8.5cm. Find <B and <C.

C 15m 12m 120o B A