Section 5.6 The Law of Sines Objective: Students will be able to: 1.Solve triangles using the Law of Sines if the measures of 2 angles and a side are given.

Slides:

Advertisements

Similar presentations

EXAMPLE 1 Solve a triangle for the SAS case Solve ABC with a = 11, c = 14, and B = 34°. SOLUTION Use the law of cosines to find side length b. b 2 = a.

Advertisements

CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve.

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.

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.

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.

7.6 Law of Sines. Use the Law of Sines to solve triangles and problems.

3.4: Using Similar Triangles

Geometry IB Date: 4/22/2014 Question: How do we measure the immeasurable? SWBAT use the Law of Sines to solve triangles and problems Agenda Bell Ringer:

SOLVING RIGHT TRIANGLES We will be given information about a triangle and then have to find the remaining sides and angles. We will develop new ways to.

Objectives Use the Law of Cosines to solve triangles.

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

1 What you will learn  How to solve triangles by using the Law of Sines if the measures of two angles and a side are given  How to find the area of a.

9.4 – The Law of Cosines Essential Question: How and when do you use the Law of Cosines?

Warm-up A farmer has a triangular field where two sides measure 450 yards and 320 yards. The angle between these two sides measures 80º. The farmer wishes.

Class Work 1.Sketch a right triangle that has acute angle , and find the five other trig ratios of . 2.Evaluate the expression without using a calculator.

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

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

Use the Law of Sines to find missing side lengths and/or

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.

1 Equations 7.3 The Law of Cosines 7.4 The Area of a Triangle Chapter 7.

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.

N AME THE FOLLOWING TRIANGLE BASED ON ANGLES AND SIDES.

8.4 Angles of Elevation and Depression Geometry. Objectives Solve a right triangle. Use right triangles to find the angles of elevation and depression.

Notes Over 8.2 Solving Oblique Triangles To solve an oblique triangle, you need to be given one side, and at least two other parts (sides or angles).

6.2 Law of Cosines *Be able to solve for a missing side or angle using law of cosines.

Law of Sines and Law of Cosines MATH 1112 S. F. Ellermeyer.

Trigonometric Ratios Day 12. Day 12 Math Review Objectives Find the sine, cosine, and tangent of an acute angle. Use trigonometric ratios to find side.

Warm-up. Law of Sines and Cosines Students will be able to apply the Law of Sines and the Law of Cosines to solve problems involving oblique triangles.

Warm Up A man looks out from a water tower and waves to his daughter who stands on the ground, 60 feet from the base of the water tower. The angle of depression.

By, Mrs. Muller.  If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent

Given Find the length of to the nearest tenth. 1. Draw a diagram and label it. A C B 2. Draw a perpendicular from AB to C. 3. Write trig equations using.

Homework Questions. LOGS Warm-up Evaluating Logs.

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.

 Solve the triangle CA B a b c.  Unit Circle Quiz  Trig Values Quiz  These will be important again in Chapter 5.

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

Bell Assignment Solve the triangle A B C C = 48° and a = 25.

Solve for x and y: 43° 75° y° x° 75° = y + 43° 75 – 43 = y 32° = y z° x and 43° are Alternate Interior Angles 43° = x.

Use isosceles and equilateral triangles

Use isosceles and equilateral triangles

Isosceles Triangles.

What does this sign mean?

Sections 6.3 & 6.4 Proving triangles are similar using AA, SSS, SAS

5.7 The Ambiguous Case for the Law of Sines

Objective: Use the law of sine. (SSA)

Unit 6: Trigonometry Lesson: Law of coSines.

Objective: To apply the Law of Sines

Some Ways to Prove Triangles Congruent

Section 18.3: Special Right Triangles

Similarity, Congruence, & Proofs

19. Law of Sines.

Warm-up Find x a) b).

a 2 = b 2 + c b c cos A These two sides are repeated.

Warm Up A man looks out from a water tower and waves to his daughter who stands on the ground, 60 feet from the base of the water tower. The angle of.

Solving OBLIQUE triangles (ssa)

Homework Questions.

Lessons 4.1 & 5.5: Introduction to Triangles

Homework Questions.

Use isosceles and equilateral triangles

Law of Sines and Cosines

Base Angles & Exterior Angles

Law of Sines Notes Over If ABC is a triangle with sides a, b, c, then according to the law of sines, or.

LAW OF SINES SECTION 7-6 Jim Smith JCHS.

Objective We will analyze congruent triangles

Section 6.5 Law of Cosines Objectives:

8-6 Using the Law of Sines Objectives:

8-5 Using the Law of Sines Objectives:

Presentation transcript:

Section 5.6 The Law of Sines Objective: Students will be able to: 1.Solve triangles using the Law of Sines if the measures of 2 angles and a side are given. 2.Find the area of a triangle if the measures of 2 sides and the included angle or the measures of 2 angles and a side are given.

Law of Sines

Example 1: Solve  ABC if A = 24°, B = 62°, and a = First, find the measure of  C. C = 180° - (24° + 62°) or 94° Use the Law of Sines to find b and c  b  c

Example 2: The angle of depression from a window of a house to the front edge of the swimming pool is 26.6°. The angle of depression from this same window to the back edge of the swimming pool is 15.3°. The length of the pool is 25 feet. If a person looks out the window, about how far is he from the front edge of the pool? *** Make a diagram of the problem. Remember that the angle of elevation is congruent to the angle of depression because they are alternate interior angles. First, find .  = 26.6° ° or 11.3° Use the Law of Sines to find d. d  The person would be about 33.7 feet from the front edge of the pool.

Example 3: Find the area of  ABC if b = 14.8, c = 10.2, and A = 54°12. K  The area of  ABC is about 61.2 square units.

Example 4: Find the area of  DEF if e = 18.6, E = 78.2°, and F = 41.3°. First find the measure of  D. D = 180° - (78.2° °) or 60.5° Then, find the area of the triangle. K  The area of  DEF is about square units.