Aim: Law of Sines Course: Alg. 2 & Trig. Aim: What is the Law of Sines and what good is it, anyway? Do Now: The length of each of the equal sides of an.

Slides:

Advertisements

Similar presentations

Aim: What is the Law of Sine? Do Now: In ∆ABC, AC = b, BC = a, and the height is (h). Find: 1. sin A 2. sin B A D B C HW: p.567 # 6,8,12,19,20,21,22,23.

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.

Solve SAA or ASA Triangles Solve SSA Triangles Solve Applied Problems

Module 8 Lesson 5 Oblique Triangles Florben G. Mendoza.

Section SOLVING OBLIQUE TRIANGLES

The Law of Sines and Law of Cosines

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.

Solve Right Triangles Ch 7.7. Solving right triangles What you need to solve for missing sides and angles of a right triangle: – 2 side lengths – or –

Aim: How do we solve problems with both law of sine and law of cosine?

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

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Aim: What to do, What to do?!? So many formulas!! Where do we begin? Do Now: Regents Question How.

Objective: Find the area of any triangle given at least three pieces of information. Process: Derive several formulas to allow use of given information.

Finding Areas with Trigonometry. Objectives I can use trigonometry to find the area of a triangle.

Honors Geometry Unit 6 Lesson 5 Finding Areas with Trigonometry.

{ Law of Sines and Cosines Trigonometry applied to triangles without right angles. 1.

April 4 th copyright2009merrydavidson CALCULATOR TODAY Happy Summer Birthdays to: Timmy Manley: 7/5 th Andrew Krasner: 8/14 th.

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.

Chapter 13 Sec 1 Right Triangle Trigonometry 2 of 12 Algebra 2 Chapter 13 Section 1 The ratios of the sides of the right triangle can be used to define.

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.

Aim: Law of Cosines Course: Alg. 2 & Trig. Aim: What is the Law of Cosines? Do Now: If the measures of two sides and the included angle of a triangle.

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?

$100 $200 $300 $400 $500 $200 $300 $400 $500 Geometric mean Pythagorean Thm. Special Right Triangles Law of Sines and Cosines Trigonometry Angles of.

Special Right Triangles Trigonometric Ratios Pythagorean Theorem Q: $100 Q: $200 Q: $300 Q: $400.

Area and the Law of Sines. A B C a b c h The area, K, of a triangle is K = ½ bh where h is perpendicular to b (called the altitude). Using Right Triangle.

Aim: Solving Linear Trig Equations Course: Alg. 2 & Trig. Aim: How do we use the principals of trigonometry to solve problems? Do Now:

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.

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).

Sec. 5.5 Law of sines.

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.

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

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

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.

Solve Right Triangles Ch 7.7. Solving right triangles What you need to solve for missing sides and angles of a right triangle: – 2 side lengths – or –

7.7 Law of Cosines. Use the Law of Cosines to solve triangles and problems.

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.

Unit 7: Right Triangle Trigonometry

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

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° =

[8-3] Trigonometry Mr. Joshua Doudt Geometry pg

Finding area of triangles. Area of a triangle Law of sines Trig ratios are generally used to find unknown measures in right triangles, but they can also.

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.

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.

Aim: What is trigonometric function?

Lesson 37 continued Get out your notes from yesterday.

Objective: To apply the Law of Sines

Warm-Up Exercises ABC Find the unknown parts of A = 75°, B 82°, c 16

…there are three trig ratios

Geometry Lesson 8 – 4 Trigonometry Objective:

…there are three trig ratios

Objectives Find the sine, cosine, and tangent of an acute angle.

8-5 The Law of Sines Geometry.

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

Solving OBLIQUE triangles (ssa)

The General Triangle C B A.

Aim: What is trigonometric function?

7.7 Law of Cosines.

Solve Right Triangles Mr. Funsch.

Objectives Determine the area of a triangle given side-angle-side information. Use the Law of Sines to find the side lengths and angle measures of a triangle.

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.

Law of Cosines.

Law of Cosines.

The General Triangle C B A.

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.

…there are three trig ratios

Right Triangle Trigonometry

Chapter 2 Trigonometry 2.4 The Cosine Law

Presentation transcript:

Aim: Law of Sines Course: Alg. 2 & Trig. Aim: What is the Law of Sines and what good is it, anyway? Do Now: The length of each of the equal sides of an isosceles triangle is a and the measure of a base angle is 15 o. Express the area of the triangle in terms of a.

Aim: Law of Sines Course: Alg. 2 & Trig. Deriving the Law of Sines The Law of Sines Used to find the measure of a side of a triangle when the measures of two angles and a side are known (a.a.s. or a.s.a.).

Aim: Law of Sines Course: Alg. 2 & Trig. Finding a Length In ∆ABC, a = 10, m  A = 30, and m  B = 50. Find b to the nearest integer. Law of Sines solve proportion: bSin30 = 10sin50 b = To nearest integer, b = 15

Aim: Law of Sines Course: Alg. 2 & Trig. Model Problem In ∆DAT, m  D = 27, m  A = 105, and t = 21. Find d to the nearest integer. solve proportion: Law of Sines dSin48 = 21sin27 d = To nearest integer, d = 12 Establish ratios based on problem: D A T t =21 105º 27º 48º

Aim: Law of Sines Course: Alg. 2 & Trig. Model Problem In ∆ABC, a = 12, sinA = 1/3, and sinC = 1/4. Find c. Solve proportion: Law of Sines 1/3c = 3 c = 9 Establish ratios based on problem:

Aim: Law of Sines Course: Alg. 2 & Trig. Model Problem In ∆ABC, m  B = 30 and m  A = 45. Find the ratio a : b. Solve proportion: Law of Sines Establish ratios based on problem:

Aim: Law of Sines Course: Alg. 2 & Trig. Model Problem (con’t) In ∆ABC, m  B = 30 and m  A = 45. Find the ratio a : b. Simplify:

Aim: Law of Sines Course: Alg. 2 & Trig. Model Problem In right triangle ABC, m  C = 90 and m  A = 56, and BC = 8.7. Find AB to the nearest tenth. C A B c b º Establish ratios based on problem: Solve proportion: c = AB To nearest tenth, d = 10.5

Aim: Law of Sines Course: Alg. 2 & Trig. Regents Prep Triangle ABC is an isosceles triangle. Its base is 16.2 cm. and one base angle is 63 o 20’. Find the length of one of the congruent sides to the nearest hundredth of a cm cm

Aim: Law of Sines Course: Alg. 2 & Trig. Model Problem A surveyor at point P sights two points X and Y that are on opposite sides of a lake. If P is 200 m. from X and 350 m. from T, and m  XPY = 40, find the distance from X to Y to the nearest meter.

Aim: Law of Sines Course: Alg. 2 & Trig. The Product Rule