Unit 34 Pythagoras’ Theorem and Trigonometric Ratios Presentation 1Pythagoras’ Theorem Presentation 2Using Pythagoras’ Theorem Presentation 3Sine, Cosine.

Slides:

Advertisements

Similar presentations

Measurement – Right Angled Triangles By the end of this lesson you will be able to identify and calculate the following: 1. The Tangent Ratio.

Advertisements

8 – 6 The Sine and Cosine Ratios. Sine and Cosine Suppose you want to fine the legs, x and y, in a triangle. You can’t find these values using the tangent.

Geometry Chapter 8.  We are familiar with the Pythagorean Theorem:

Copyright © Cengage Learning. All rights reserved. Trigonometric Functions: Right Triangle Approach.

Textbook: Chapter 13. ** Make sure that your calculator is set to the proper mode**

Solving Right Triangles Given certain measures in a right triangle, we often want to find the other angle and side measures. This is called solving the.

Trigonometry Chapters Theorem.

Solving Right Triangles

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 Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.

45 ⁰ 45 – 45 – 90 Triangle:. 60 ⁰ 30 – 60 – 90 Triangle: i) The hypotenuse is twice the shorter leg.

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 –

8.3 Solving Right Triangles

EXAMPLE 1 Finding Trigonometric Ratios For PQR, write the sine, cosine, and tangent ratios for P. SOLUTION For P, the length of the opposite side is 5.

Lesson 1: Primary Trigonometric Ratios

Geometry Notes Lesson 5.3A – Trigonometry T.2.G.6 Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles.

Do Now Find the missing angle measures. 60° 45°

Geometry Notes Lesson 5.3B Trigonometry

Friday, February 5 Essential Questions

Further Trigonometry Learning Outcomes  Calculate distances and angles in solids using plane sections and trig ratios  Be able to sketch graphs of sine,

Solving Right Triangles

How do I use the sine, cosine, and tangent ratios to solve triangles?

A grain auger lifts grain from the ground to the top of a silo. The greatest angle of elevation that is possible for the auger is 35 o. The auger is 18m.

Right Triangle Trigonometry Sine, Cosine, Tangent.

7.2 Finding a Missing Side of a Triangle using Trigonometry

TRIGONOMETRY Lesson 1: Primary Trigonometric Ratios.

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

The Right Triangle Right Triangle Pythagorean Theorem

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 –

© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 10 Geometry.

4-57. To find out how high Juanisha climbed up stairs, you need to know more about the relationship between the ratios of the sides of a right triangle.

Using SOHCAHTOA Trigonometry. In each of the following diagrams use SIN to find the angle x correct to 1 decimal place x x x

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

Trigonometry Chapters Theorem.

7.5 and 7.6 Trigonometric Ratios The Legend of SOH CAH TOA...Part 1 The Legend of SOH CAH TOA...Part 1.

Opener. The Trigonometric Functions we will be looking at SINE COSINE TANGENT.

9.5: Trigonometric Ratios. Vocabulary Trigonometric Ratio: the ratio of the lengths of two sides of a right triangle Angle of elevation: the angle that.

Trigonometry. 2 Unit 4:Mathematics Aims Introduce Pythagoras therom. Look at Trigonometry Objectives Investigate the pythagoras therom. Calculate trigonometric.

A Quick Review ► We already know two methods for calculating unknown sides in triangles. ► We are now going to learn a 3 rd, that will also allow us to.

Area of Triangles Non Right-Angled Triangle Trigonometry By the end of this lesson you will be able to explain/calculate the following: 1.Area of Right-Angled.

OBJECTIVE 8.3 TRIGONOMETRY To use the sine, cosine, and tangent ratios to determine the side lengths and angle measures in right triangles.

 Right Triangle – A triangle with one right angle.  Hypotenuse – Side opposite the right angle and longest side of a right triangle.  Leg – Either.

April 21, 2017 The Law of Sines Topic List for Test

Lesson: Introduction to Trigonometry - Sine, Cosine, & Tangent

The Trigonometric Functions

Trigonometry Review.

Trigonometry Ratios in Right Triangles

Calculating Sine, Cosine, & Tangent (5.9.1)

Pythagoras’ Theorem – Outcomes

7-6 Sine and Cosine of Trigonometry

Angles of Elevation and Depression

Learning Journey – Pythagoras’ Theorem and Trigonometry

Inverse Trigonometric Functions

6-3: Law of Cosines

MM3 – Similarity of two-dimensional Figures, Right-Angled Triangles

CHAPTER 10 Geometry.

Copyright © Cengage Learning. All rights reserved.

Applying Relationships in Special Right Triangles

Aim: How do we review concepts of trigonometry?

Trigonometry Ratios in Right Triangles

Solve Right Triangles Mr. Funsch.

7-5 and 7-6: Apply Trigonometric Ratios

Law of Sines and Cosines

Right Triangle Trigonometry

Geometry Section 7.7.

Similar Triangles Review

Pythagoras’ Theorem.

Trigonometry Ratios in Right Triangles

Trigonometric Ratios Geometry.

Copyright © Cengage Learning. All rights reserved.

Presentation transcript:

Unit 34 Pythagoras’ Theorem and Trigonometric Ratios Presentation 1Pythagoras’ Theorem Presentation 2Using Pythagoras’ Theorem Presentation 3Sine, Cosine and Tangent Ratios Presentation 4 Finding the Lengths of Sides in Right Angled Triangles

Unit Pythagoras’ Theorem

Pythagoras’ theorem states that for any right angled triangle. Example 1 What is the length of a (the hypotenuse)? Solution ? ? ? ? ? ? ? Example 2 Find the length of side x. Solution ? ? ? ? ? ? ? ? ?

Unit Using Pythagoras’ Theorem

Example 1 Find the length of the side marked x in the diagram. Solution In triangle ABC In triangle ACD Example 2 Find the value of x as shown in the diagram, giving the lengths of the two unknown sides Solution Pythagoras’ Theorem gives So Here we see how Pythagoras’ Theorem can be used to solve different problems. ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? C B A D

Unit Sine, Cosine and Tangent

For a right angled triangle, the sine, cosine and tangent of the angle θ are defined as:

Example 1 For the triangle and angle θ state which side is (a)HypotenuseCB (b)AdjacentAC (c)OppositeAB ? ? ?

Example 2 For the triangle below, what is the value of (a) (b) (c) ? ? ? ? ? ? ? ? ?

Unit Finding the Lengths of sides in Right Angled Triangles

Example 1 Find the length of the side marked x in the triangle. Solution So ? ? ? ? ? (to 1 d. p.)

Example 2 Find the length of the side marked x in the triangle Solution So ? ? ? ? ? (to 1 d. p.)

Example 3 For the diagram calculate to 3 significant figures (a)The length of FI (b)The length of EI (c)The area of EFGH Solution (a) (b) (c) ? ? ? ? ? ? ? ? ? ? ?