Pre Calculus 11 Section 2.1b Special Triangles

Slides:

Advertisements

Similar presentations

Special Right Triangles

Advertisements

Measurement Pythagorean Relationship 3 (Finding the length of an unknown leg)

Pythagorean Relationship 2 (Finding the length of the Hypotenuse)

Trigonometry Ratios.

Values: Respect, Integrity, Mathematical Thinking GOAL: MAXIMIZE UNDERSTANDING.

Warm-up 1.) What types of triangles have you studied? What are characteristics of each one? 2.) Given 2 sides of a triangle find the third side a.)b.)

Measurment and Geometry

Special Right Triangles

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.

Lesson 56: Special Right Triangles

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

Slide The Pythagorean Theorem and the Distance Formula  Special Right Triangles  Converse of the Pythagorean Theorem  The Distance Formula: An.

Geometry Section 9.4 Special Right Triangle Formulas

Bell Ringer Get out your 10.5/10.7 homework assignment and formula sheet Get out your notebook and prepare to take notes on Section 11.2 What do you know.

Section 3-5 p. 137 Goal – to solve problems using the Pythagorean Theorem.

REVIEW OF ROOTS 4 This is a collection of warm-ups and practice from class. 4 Click to advance the slide and follow along. 4 You can use the scroll bar.

7-3 Special Right Triangles

The World Of Triangles. Triangles A triangle is a 3- sided polygon. Every triangle has three sides and three angles. When added together, the three angles.

Types of 2 D Shapes and There Properties 1)A shape with 3 sides is called a triangle 2)A shape with 4 sides is called a quadrilateral 3)The general term.

Geometry Section 7.4 Special Right Triangles. 45°-45°-90° Triangle Formed by cutting a square in half. n n.

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.

THE NATURE OF GEOMETRY Copyright © Cengage Learning. All rights reserved. 7.

Right Triangles and Trigonometry Chapter Geometric Mean  Geometric mean: Ex: Find the geometric mean between 5 and 45 Ex: Find the geometric mean.

Triangle A polygon with three sides and three angles. A triangle can be names by its’ side lengths and angles. – Side lengths: isosceles, equilateral,

7.4.1 SPECIAL RIGHT TRIANGLES Chapter 7: Right Triangles and Trigonometry.

College Algebra Section R.3 Geometry Review Objectives of this Section Use the Pythagorean Theorem and Its Converse Know Geometry Formulas.

Intro to radians and unit circle F-TF.1 F-TF.2 ANGLES AND ANGLE MEASURE.

TRIANGLES AND TYPES OF TRIANGLES. A triangle has three sides.

8.2 Special Right Triangles. Side lengths of Special Right Triangles Right triangles whose angle measures are 45°-45°-90° or 30°- 60°-90° are called special.

Special Right Triangles

Honors Geometry Section 5.5 Special Right Triangle Formulas.

Why does the line y = x only have one slope? What is true about all of the triangles? How does this relate to Pythagorean Theorem?

5.2 What If The Triangle Is Equilateral? Pg. 6 Equilateral Triangles.

Triangle Review A scalene triangle has no sides and no angles equal. An isosceles triangle has two sides and two angles equal. An equilateral triangle.

Classifying Triangles How many degrees can be found in all triangles? 180 We can classify triangles 2 ways: By their angles By their sides.

Refresh Your Skills for Chapter 12.  If you split an equilateral triangle in half along an altitude, you create two right triangles with angles of 30°,

Splash Screen. Then/Now You used the Pythagorean Theorem to find missing lengths in right triangles. Find trigonometric ratios using right triangles.

8-6 and 8-7 Square Roots, Irrational Numbers, and Pythagorean Theorem.

Special Right Triangles SWBAT find unknown lengths in 45°, 45°, 90° and 30°, 60°, 90° triangles.

– Use Trig with Right Triangles Unit IV Day 2.

Angles In Triangles Types of Triangles Isosceles triangle

Lesson 35: Special Right Triangles and the Pythagorean Theorem

Isosceles, Equilateral, Right Triangles

HMWK: p. 554, #s 12 – 25 all Game Plan: Today I will be able to use special right triangles to calculate side lengths. Warm-up: Simplify the following.

Special Right Triangles

Warm-Up Find x. 2x+12 =6 12x=24 √25 = x.

Special Right Triangles

Grade 10 Academic (MPM2D) Unit 5: Trigonometry Solving Right Triangles

Triangles Unit 3 Review Material

7.1 Apply the Pythagorean Theorem

Calculating Sine, Cosine, & Tangent (5.9.1)

Learning Journey – Pythagoras’ Theorem and Trigonometry

Angles In Triangles Types of Triangles Isosceles triangle

Section 4.5 isosceles & equilateral triangles

7-5 Areas of Regular Polygons

Angles In Triangles Types of Triangles Isosceles triangle

6-3 The Pythagorean Theorem Pythagorean Theorem.

Section 2.4 Cosine Law © Copyright all rights reserved to Homework depot:

7-5 Areas of Regular Polygons

Lesson 14.2 Special Triangles pp

Symmetry in Circles Isosceles triangles have two equal sides and two equal angles. e° f° b° 30° n° e = (180 – 30)°  2 m° a° 70° = 75° 110° a = 70°

right triangles Some right triangles are used so frequently that it is helpful to remember some of their properties. These triangles are called.

Section 2.2 Trig Ratios with Any Angle

Section 3.2 Unit Circles with Sine and Cosine

Similar Triangles Review

The Pythagorean Theorem

TWO SIDES-ANGLE AND PERIMETER-RATIO

The Super 9 – Angles GOOD – calculate the missing angles

Presentation transcript:

Pre Calculus 11 Section 2.1b Special Triangles © Copyright all rights reserved to Homework depot: www.BCMath.ca

i) What are Special Triangles? There are two types of special triangles: 30°, 60°, 90° triangle (Equilateral Triangle) and 45°, 45°, 90° triangle (Isosceles-Right Triangle) Equilateral Triangle Isosceles-Right Triangle All sides and angles are equal Two sides are equal and one angle Is equal to 90° Cut it in half Use Pythagorean Thm. to find the hypotenuse of the triangle Use Pythagorean Thm. to find the height of the triangle Isoceles  2 equal angles © Copyright all rights reserved to Homework depot: www.BCMath.ca

Special triangles can be used to find the exact value of sine/ cosine/tangent of basic angles like: 30°, 45°, 60°, and 90° Rather than obtaining a decimal representation, we get the exact value as a fraction using special triangles © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: Use the special triangles to determine the exact value of each angle: © Copyright all rights reserved to Homework depot: www.BCMath.ca

Simply use the ratios of the triangle to find the lengths When one side of a special triangle is given, the lengths of the other two sides can be found without calculations Simply use the ratios of the triangle to find the lengths Ex: Find the lengths of the missing sides Correspond the sides with the special triangle Find “k”

Practice: Use the special triangles to determine the lengths of the unknown sides 45° 5 r q 45° m n 60° 30° 4.5 d c 60° 30° s t 10

Ex: Find the missing lengths: 1. Special Triangle 2. Isosceles Triangle © Copyright all rights reserved to Homework depot: www.BCMath.ca

Example 3: An equilateral triangle is inscribed in a circle with a diameter of 20 cm. Determine the area of the triangle in exact form