UNIT 3 RIGHT TRIANGLE TRIGONOMETRY Vocabulary Builder Daily

UNIT 3: RIGHT TRIANGLE TRIGONOMETRY Vocabulary Builder

Daily Agenda Similar Triangles leg Pythagorean Theorem Square Root Hypotenuse Simplest radical form Variable 45 -45 -90 Triangle 30 -60 -90 Triangle

Daily Agenda

UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3. 1 Trigonometric Ratios

Daily Agenda 3. 1 Trigonometric Ratios square root perfect square radical expression radicand perfect square

Daily Agenda 3. 1 Trigonometric Ratios 5 8 30 18 Check for Understanding 14 23

Daily Agenda 3. 1 Trigonometric Ratios right triangle equals hypotenuse side lengths

Daily Agenda 3. 1 Trigonometric Ratios Example 2/ Check for Understanding 13) 14) 15)

Daily Agenda 3. 1 Trigonometric Ratios We can use the Pythagorean Theorem to determine if 3 given numbers represent the sides of a right triangle. Example 3: A. 5, 5, 10 25 + 25 = 100 B. 9, 12, 15 81 + 144 = 225 YES C. 6, 8, 10

Daily Agenda 3. 1 Trigonometric Ratios Dividing into 2 Similar Sub-Triangles

Daily Agenda 3. 1 Trigonometric Ratios Dividing into 2 Similar Sub-Triangles 15: 39 36: 39 15: 36

Daily Agenda 3. 1 Trigonometric Ratios Dividing into 2 Similar Sub-Triangles

Daily Agenda 3. 1 Trigonometric Ratios hypotenuse adjacent opposite

Daily Agenda 3. 1 Trigonometric Ratios Example 4

Daily Agenda 3. 1 Trigonometric Ratios Check for Understanding

Daily Agenda 3. 1 Trigonometric Ratios trigonometric ratio SOH CAH TOA right length acute

Daily Agenda

Daily Agenda 3. 1 Trigonometric Ratios Example 5 SOH CAH TOA

5 Question Wrap-Up ■

UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3. 2 Finding Sides and Angles of Right Triangles

Daily Agenda 3. 2 Missing Sides and Angle functions angle output input

Daily Agenda 3. 2 Missing Sides and Angle x x x

Daily Agenda 3. 2 Missing Sides and Angle Check for Understanding x

Daily Agenda 3. 2 Missing Sides and Angle sin-1 Example 2 cos-1 tan-1

Daily Agenda 3. 2 Missing Sides and Angle Example 3

5 Question Wrap-Up ■

UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3. 3 Sine and Cosine of Complementary Angles

3. 3 Sine and Cosine of Complementary Angle Daily Agenda What am I learning today? ˚ 90 x • G. SRT. 7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? 180˚ 90˚ complementary x • Find the complement of sine and cosine How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door opposite angle cosine

3. 3 Sine and Cosine of Complementary Angle Daily Agenda What am I learning today? • G. SRT. 7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? • Find the complement of sine and cosine How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door Check for Understanding

3. 3 Sine and Cosine of Complementary Angle Daily Agenda What am I learning today? • G. SRT. 7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? • Find the complement of sine and cosine How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door Example 2

3. 3 Sine and Cosine of Complementary Angle Daily Agenda Example 2 continued What am I learning today? • G. SRT. 7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? Then m Q = 60˚ • Find the complement of sine and cosine How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door Sin A and Cos B are the same which means the complement of sine and cosine are equal.

3. 3 Sine and Cosine of Complementary Angle Daily Agenda What am I learning today? • G. SRT. 7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? • Find the complement of sine and cosine How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door Example 3

3. 3 Sine and Cosine of Complementary Angle Daily Agenda What am I learning today? • G. SRT. 7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? Example 4 13 5 C • Find the complement of sine and cosine How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door A 37 13 12 B A 35 H 37 12 T

3. 3 Sine and Cosine of Complementary Angle Daily Agenda What am I learning today? • G. SRT. 7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? Check for Understanding 10 • Find the complement of sine and cosine How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door T. O. T. D. Slide

UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3. 4 Application of Trig

3. 4 Solve Right Triangles using Daily Agenda Trigonometric Ratios What am I learning today? • G. SRT. 8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? • Use the Pythagorean Theorem to Solve Right Triangles • Use Trigonometric Ratios to Solve Right Triangles How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door solve side lengths angle The length of two sides The length of 1 side and 1 acute angle The length of 1 side and 1 trigonometric ratio

3. 4 Solve Right Triangles using Daily Agenda Trigonometric Ratios What am I learning today? • G. SRT. 8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? • Use the Pythagorean Theorem to Solve Right Triangles • Use Trigonometric Ratios to Solve Right Triangles How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door 9. 42 9. 4 19˚ 71˚ R = 90 – 19. 2 = 70. 8˚

3. 4 Solve Right Triangles using Daily Agenda Trigonometric Ratios What am I learning today? • G. SRT. 8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems Example 2 What am I going to do today? • Use the Pythagorean Theorem to Solve Right Triangles • Use Trigonometric Ratios to Solve Right Triangles How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door 3. 92 6. 27 58˚ C = 90 – 32 = 58˚

3. 4 Solve Right Triangles using Daily Agenda Trigonometric Ratios What am I learning today? • G. SRT. 8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? • Use the Pythagorean Theorem to Solve Right Triangles • Use Trigonometric Ratios to Solve Right Triangles How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door angle of elevation angle of depression

3. 4 Solve Right Triangles using Daily Agenda Trigonometric Ratios What am I learning today? • G. SRT. 8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? • Use the Pythagorean Theorem to Solve Right Triangles • Use Trigonometric Ratios to Solve Right Triangles How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door Example 3

3. 4 Solve Right Triangles using Daily Agenda Trigonometric Ratios What am I learning today? • G. SRT. 8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? • Use the Pythagorean Theorem to Solve Right Triangles • Use Trigonometric Ratios to Solve Right Triangles How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door Check for Understanding

3. 4 Solve Right Triangles using Daily Agenda Trigonometric Ratios What am I learning today? Example 4 • G. SRT. 8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? • Use the Pythagorean Theorem to Solve Right Triangles • Use Trigonometric Ratios to Solve Right Triangles How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door 618. 75 ft

3. 4 Solve Right Triangles using Daily Agenda Trigonometric Ratios What am I learning today? • G. SRT. 8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems Example 5 What am I going to do today? • Use the Pythagorean Theorem to Solve Right Triangles • Use Trigonometric Ratios to Solve Right Triangles How will I show you that I’ve learned it? • 5 Question Daily Assessment • Daily Ticket out the Door 991. 86 ft