special right triangles chapter 8 section 3 learning goal: use properties of 45°-45 °-90 °, and...

12

Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles We make a living by what we get, but we make a life by what we give. -- Winston Churchill

Upload: giles-flowers

Post on 13-Jan-2016

217 views

Category:

Documents

1 download

Report

Download

Tags:

Embed Size (px):

TRANSCRIPT

Page 1: Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles We make a living by what we

Special Right Triangles

Chapter 8 Section 3

Learning Goal: Use properties of 45°-45 °-90 °, and

30 °-60 °-90 ° Triangles

We make a living by what we get, but we make a life by what we give. -- Winston

Churchill

Page 2: Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles We make a living by what we

45°-45°-90° Triangles Special Right Triangle

x

x d d2 = x2 + x2

d2 = 2x2Simplify:

√d2 = √ 2x2

d = x√ 2

Three sides of lengths x, x, x√2

What did we learn about

ratios of sides?

Ratio of a 45°-45°-90° triangle is:

1 : 1 : √2

45°

Page 3: Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles We make a living by what we

45°-45°-90° Triangles

Find the missing side

a = 4√2 cm

6√245°

6

Page 4: Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles We make a living by what we

45°-45°-90° Triangles

38

45°21

14

Page 5: Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles We make a living by what we

Special Right TrianglesWALLPAPER TILING The wallpaper in the figure can be divided into four equal square quadrants so that each square contains 8 triangles. What is the area of one of the squares if the hypotenuse of each 45°–45°–90° triangle measures millimeters?

A = 24.5 mm

Page 6: Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles We make a living by what we

30°-60°-90° TrianglesConsider an equilateral ∆

2x

x

2x

x

a

60° 60°

30°

a2 = (2x)2 – x2

Simplify: a2 = 4x2 – x2

a2 = 3x2

√a2 = √3x2

a = x√3Three sides of lengths x, 2x, x√3

Ratios of sides?

Ratio of a 30°-60°-90° triangle is:

1 : √3 : 2

Page 7: Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles We make a living by what we

30°-60°-90° Triangles

Find the missing sides

60°

30°5

10

5√3

8√33

4

Page 8: Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles We make a living by what we

30°-60°-90° Triangles

68

30°

4√2

60°

60°

Find the Altitude of the Δ

Page 9: Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles We make a living by what we

Special Right Triangles

Refer to the figure. Find x and y.

Page 10: Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles We make a living by what we

Special Right Triangles

60 cm

The length of the diagonal of a square is cm. Find the perimeter of the square.

Page 11: Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles We make a living by what we

Special Right Triangles

The side of an equilateral triangle measures 21 inches. Find the length of an altitude of the triangle.

Page 12: Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles We make a living by what we

Homework

Special Right Triangles 45-45-90, 30-60-90

入っているもの...0 90 45 30 15 60 75 0 90 45 30 15 60 75 0 90 45 30 15 60 75 0 90 45 30 15 60 75 0 90 45 30 15 60 75 0 90 45 30 15 60 75 0 90 45 30 15 60 75 0 90 45 30 15 60

45 45-90 Right Triangle

4.2 Trigonometric Functions: The Unit Circle...The Unit Circle Using what we found with the 45 45 90 triangles and the 30 60 90 triangles, we can complete what is referred to as the

PROJETO CURRICULAR - AERDLnsite.aerdl.eu/.../DocsAgrupamento/AERDL/Doc_Gerais/PCA_.pdf · 2020. 2. 27. · Matemática 300 90+90+45 90+90 90+90 Física e Química 200 90+90+45 90+45

Special Right Triangles. Right triangles have one 90 o angle The longest side is called the HYPOTENUSE…

Lesson 56: Special Right Triangles 30°- 60°- 90°

9.2 Special Right Triangles - WordPress.com · 09.04.2018 · 9.2 Special Right Triangles There are two types of special right triangles; 45-45-90 Triangles and 30-60-90 Triangles

45 45-90 triangles

gov.md · Merceologie 41630 110 60 20 20 40 40 50 1 Mediul înconjurător 52 90 90 45 45 45 45 1 Ecologia şi protecţia mediului 52110 90 90 45 45 45 45 1 Ştiinţa fizicii 53 60

8-3 Special Right Triangles You used properties of isosceles and equilateral triangles. Use the properties of 45°-45°-90° triangles. Use the properties

· 160616,0 90 45 45 90 90 45 45 45 90 45 90 90 45 90 90 90 45 30 Orp 3 460 45 45 45 45 45 2/ 1/ 5/ 8 4 5 Momignies Union Autre Eglise - Doubla e Wallon

Special Right Triangles Objectives: 1.To use the properties of 45-45-90 and 30-60-90 right triangles to solve problems

Bell Ringer. 30-60-90 Triangles A Right Triangle with angle measures of 30, 60, and 90 are called 30-60-90 triangles

Geometry 8.2 Special Right Triangles. Objectives/DFA/HW Objectives SWBAT use properties of 45 o -45 o -90 o & 30 o -60 o -90 o triangles. Why? Ex. – To

Grant County Schools Home › Downloads › NOTES U6...450 45 - x 450 45 - 90 300 3 30 - 60 - 600 90 Practice 6 - 2 "Special Right Triangles" Find the value of the variable. 600 300

Z/ZU 45/75-90/110 ZL/ZLU 45/75-90/110 ZN/ZNU 45/75-90/110

Special Right Triangles 45:45:90 Right Triangles

Geometry Honors: Unit 8 Day 2 Special Right Trianglesjrsullivan4.weebly.com/uploads/3/9/0/7/39076379/gh-u8d2... · 2018-10-17 · Special Right Triangles Developing the 45-45-90 Triangle

ITALIAN BATH CONCEPT · 2014-05-07 · su misura 120 140 230 230 190 190 210 45 45 45 45 45 45 70 70 70 90 90 90 90 90 90 50 50 70 5070 50 50 50 51 51 51 51 51 51 Composizione ALBA

8-2 30-60-90 Triangles

1 1 1 1 1 1 2 90° 45° 2 90° 90° 45°

Special Right Triangles. Use properties of 45° - 45° - 90° triangles Use properties of 30° - 60° - 90° triangles

Special Right Triangles and Trigonometry - WikispacesRight+Triangles... · Special Right Triangles and Trigonometry ... Act. 9 (45-45-90 Triangles Part 2), ... 5.1, Act. 1 (Right

class range joinery machines - SCM Group...Blades tilting mm -46 ÷ +46 90 ÷ 45 90 ÷ 45 90 ÷ 45 90 ÷ 45 90 ÷ 45 Max. saw blade diameter 550 550* 400 400 350 315 Max. saw blade

Mathematics II Name of unit – Right Triangle Trigonometry II_Unit 2-Right...Determine the lengths of sides of 45 -45 -90 triangles. Opening – Warm-up: √50 + √32 Teacher models

Special Right Triangles 30:60:90 Right Triangles

Geometry Academic UNIT QUESTION: What patterns can I find in right triangles? Standard: MM2G1, MM2G2 Today’s Question: How do we solve 45°-45°-90° right

Two Special Right Triangles 45°- 45°- 90° 30°- 60°- 90°

5.8 Special Right Triangles Day 1: 45-45-90...5.8 Special Right Triangles Day 1: 45-45-90 Part 1: Follow the instructions below for the next three examples. A. In the given square,

45˚- 45˚- 90˚ Triangles Drawing the diagonal of a square separates it into two 45˚- 45˚- 90˚ triangles. Because it’s a square, the legs of the triangle

Website practice 45 triangles

Luda (Taian) Industrial Co. Ltd.ludataiwan.com/download/pdf/luda_catalogue.pdf · DIN 2616 DIN 2617 DIN 2609 xxs xxs 90 45 90 45 90 45 90 45 45 90 45 114383 HGJ514-87 HGJ528-90 HGUIO-B8

*You will be able to find the lengths of sides of special right triangles 45-45-90 And 30-60-90

2-Directional Boundary Microphone FR-1000€¦ · 0°-45° +45°-90°-135° +135° +90° 0°-45° +45°-90°-135° +135° +90° Mode Switching The DIP switches on the backside of

Section 7 – 3 Special Right Triangles Objectives: To use the properties of 45-45-90 triangles To use the properties of 30-60-90 triangles