The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right...

14
The Pythagorean Theorem

Transcript of The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right...

Page 1: 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.

The Pythagorean Theorem

Page 2: 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.

The Right Triangle

A right triangle is a triangle

that contains one right

angle.

A right angle is 90o

Right Angle

Page 3: 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.

Parts of a Right Triangle

Leg

Leg

Hypotenuse

Page 4: 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.

The Pythagorean Theorem

a2 + b2 = c2

a

b

c

Page 5: 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.
Page 6: 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.

Example 1

Find the length of the hypotenuse.

3

4c

Page 7: 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.

Example 2

Find the length of the hypotenuse.

6

8c

Page 8: 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.

Example 3

Find the length of the hypotenuse

12

16

c

Page 9: 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.

Example 4

Find the length of the unknown side

12

13b

Page 10: 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.

Example 5

Find the length of the unknown side.

1715

a

Page 11: 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.

Example 7

Find the length of the unknown side.

25

24

b

Page 12: 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.

Pythagorean Triple

All of the side lengths of the triangles we have looked at form Pythagorean Triples.

If the side lengths of a right triangle are all whole numbers, they are called Pythagorean Triples.

Page 13: 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.

Pythagorean Triples

List the Pythagorean Triples we have discussed.

Page 14: 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.

Right Angle Trigonometry. Labeling a Right Triangle In trigonometry, we give each side a name according to its position in relation to any given angle.

Right Angle Trigonometry. Labeling a Right Triangle In trigonometry, we give each side a name according to its position in relation to any given angle.

Right Angle Trigonometry - Rochester Institute of … opposite angle A. II. Right Triangle Facts and Examples 1. Hypotenuse – the side opposite the right angle, side c. 2. Pythagorean

Right Angle Trigonometry - Rochester Institute of … opposite angle A. II. Right Triangle Facts and Examples 1. Hypotenuse – the side opposite the right angle, side c. 2. Pythagorean

If none of the angles of a triangle is a right angle, the triangle is called oblique. All angles are acute Two acute angles, one obtuse angle.

If none of the angles of a triangle is a right angle, the triangle is called oblique. All angles are acute Two acute angles, one obtuse angle.

Chapter 2 Right Triangle Trigonometryaplustestbank.eu/sample/Solution-Manual-for... · Chapter 2 Right Triangle Trigonometry 2.1 Trigonometric Functions of an Acute Angle 2.1 Practice

Chapter 2 Right Triangle Trigonometryaplustestbank.eu/sample/Solution-Manual-for... · Chapter 2 Right Triangle Trigonometry 2.1 Trigonometric Functions of an Acute Angle 2.1 Practice

Bell Ringer. Tangent Ratios A trigonometric ratios is a ratio of the lengths of two sides of a right triangle. For any acute angle of a right triangle,

Bell Ringer. Tangent Ratios A trigonometric ratios is a ratio of the lengths of two sides of a right triangle. For any acute angle of a right triangle,

Right Triangle Trigonometry - PreCalculusCoach.com...Right Triangle Trigonometry Right angle trigonometry is the trigonometry of a right-angled triangle. A right-angled triangle is

Right Triangle Trigonometry - PreCalculusCoach.com...Right Triangle Trigonometry Right angle trigonometry is the trigonometry of a right-angled triangle. A right-angled triangle is

Right Triangles And the Pythagorean Theorem. Legs of a Right Triangle Leg -the two sides of a right triangle that form the right angle Leg.

Right Triangles And the Pythagorean Theorem. Legs of a Right Triangle Leg -the two sides of a right triangle that form the right angle Leg.

hypotenuse. Relative to the angle θ, side adjacent side ... · TRIGONOMETRY REVIEW TRIGONOMETRIC RATIOS If one of the angles of a triangle is 90º (a right angle), the triangle is

hypotenuse. Relative to the angle θ, side adjacent side ... · TRIGONOMETRY REVIEW TRIGONOMETRIC RATIOS If one of the angles of a triangle is 90º (a right angle), the triangle is

This is a right triangle: We call it a right triangle because it contains a right angle.

This is a right triangle: We call it a right triangle because it contains a right angle.

Triangle Angle Sum Theorem Isosceles Triangles Equilateral Triangle.

Triangle Angle Sum Theorem Isosceles Triangles Equilateral Triangle.

7.1 Right Triangle Trigonometry. A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle is called.

7.1 Right Triangle Trigonometry. A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle is called.

PC 5.1 right triangle trig · 2015. 4. 6. · Vocabularv: Angle of Elevation and Angle of Depression Angle of Elevation: Example: Mount Rushmore Angle of Depression: L Example: Grand

PC 5.1 right triangle trig · 2015. 4. 6. · Vocabularv: Angle of Elevation and Angle of Depression Angle of Elevation: Example: Mount Rushmore Angle of Depression: L Example: Grand

Lesson 18.2: Right Triangle Trigonometry · Chapter 2: Right Triangle Trigonometry Page 2 Consider any two right triangles. If the triangles have one other equal angle, x say, then

Lesson 18.2: Right Triangle Trigonometry · Chapter 2: Right Triangle Trigonometry Page 2 Consider any two right triangles. If the triangles have one other equal angle, x say, then

Right Triangle Geometry - Oak Park Geometry Classes … CHAPTER 4 Right Triangle Geometry 4.1 Interior and Exterior Angles of a Triangle Triangle Sum, Exterior Angle, and Exterior

Right Triangle Geometry - Oak Park Geometry Classes … CHAPTER 4 Right Triangle Geometry 4.1 Interior and Exterior Angles of a Triangle Triangle Sum, Exterior Angle, and Exterior

Trigonometry for Any Angle. SineCosineTangentCosecantSecantCotangent Abbreviation Reciprocal Function Co-function Right Triangle Definition Unit Circle.

Trigonometry for Any Angle. SineCosineTangentCosecantSecantCotangent Abbreviation Reciprocal Function Co-function Right Triangle Definition Unit Circle.

1 Right Triangle Trigonometry. 2 Take a look at the right triangle, with an acute angle, , in the figure below. Notice how the three sides are labeled.

1 Right Triangle Trigonometry. 2 Take a look at the right triangle, with an acute angle, , in the figure below. Notice how the three sides are labeled.

9 Trigonometric Ratios and Functions...Section 9.1 Right Triangle Trigonometry 463 Evaluating Trigonometric Functions In a right triangle, θ is an acute angle and sin θ = 4— 7.

9 Trigonometric Ratios and Functions...Section 9.1 Right Triangle Trigonometry 463 Evaluating Trigonometric Functions In a right triangle, θ is an acute angle and sin θ = 4— 7.

Pythagoras’ Theorem€¦ · PYTHAGORAS’ THEOREM (Chapter 2) 35 A right angled triangle is a triangle which has a right angle as one of its angles. The side opposite the right

Pythagoras’ Theorem€¦ · PYTHAGORAS’ THEOREM (Chapter 2) 35 A right angled triangle is a triangle which has a right angle as one of its angles. The side opposite the right

missgillett.weebly.com · 2019-05-01 · Exercise 8D: Pythagoras' A right angled triangle is a triangle which has a right angle as one of its angles. The side opposite the right angle

missgillett.weebly.com · 2019-05-01 · Exercise 8D: Pythagoras' A right angled triangle is a triangle which has a right angle as one of its angles. The side opposite the right angle

1 4-3 Right Triangle Trigonometry Pre-Calculus. 2 The six trigonometric functions of a right triangle, with an acute angle , are defined by ratios of.

1 4-3 Right Triangle Trigonometry Pre-Calculus. 2 The six trigonometric functions of a right triangle, with an acute angle , are defined by ratios of.