UNIT 3: RIGHT TRIANGLE TRIGONOMETRY Vocabulary Builder
44 Slides2.65 MB
UNIT 3: RIGHT TRIANGLE TRIGONOMETRY Vocabulary Builder
Daily Agenda Similar Triangles Square Root leg Pythagorea n Theorem Simplest radical form 45-45-90 Triangle Hypotenus e Variable 30-60-90
Daily Agenda
Daily Agenda
UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3.1 Trigonometric Ratios
Daily 3.1 Agenda Trigonometric Ratio square root perfect square radical expression radicand perfect square
Daily 3.1 Agenda Trigonometric Ratio 5 30 8 18 14 23 Check for Understanding ๐ ๐ 2 10 3 3 ๐ ๐
Daily 3.1 Agenda Trigonometric Ratio right triangle equals hypotenuse side lengths
Daily 3.1 Trigonometric Agenda Example 2/ Check for Understanding 13) 14) 2 2 4 8 ๐ฅ 2 1 6 64 ๐ฅ 2 8 0 ๐ฅ 2 4 5 ๐ฅ Ratio 15) 2 2 ๐ฅ2 3.9 2 112 2 ๐ฅ2 15.21 121 2 6 3 ๐ฅ 3 6 9 ๐ฅ 4 5 ๐ฅ 2 3 5 ๐ฅ ๐ฅ2 105.79 ๐ฅ 10.29
Daily 3.1 Trigonometric Ratio Agenda 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 50 100 NO C. 6, 8, 10 B. 9, 12, 15 81 144 225 225 225 YES D. 4, 6,
Daily 3.1 Trigonometric Ratio Agenda Dividing into 2 Similar SubTriangles ๐น๐ผ๐บ ๐บ๐ผ๐ป
Daily 3.1 Trigonometric Ratio Agenda Dividing into 2 Similar SubTriangles 15:39 :36 :15 36:39 :36 :15 15:36 : :
Daily 3.1 Trigonometric Ratio Agenda Dividing into 2 Similar SubTriangles 3. Use the values of the ratios you calculated to find the length of and
Daily 3.1 Agenda Trigonometric Ratio hypotenuse adjacent opposite
Daily 3.1 Trigonometric Agenda Example 4 ๐๐ ๐๐ ๐๐ Ratio
Daily 3.1 Trigonometric Agenda Check for Understanding ๐ป๐ ๐๐ผ ๐ป๐ผ Ratio
Daily 3.1 Trigonometric trigonometric ratio Agenda SOH CAH TOA right length acute Ratio
Daily Agenda
Daily 3.1 Trigonometric Agenda Example 5 SOH CAH TOA Ratio ๐๐๐ 20 4 ยฟ ยฟ ๐ด๐ท๐ฝ 15 3 ๐๐๐ 16 8 ยฟ ยฟ ๐ด๐ท๐ฝ 30 15 ๐๐๐ 14 7 ยฟ ยฟ 24 48 ๐ด๐ท๐ฝ ๐๐๐ 15 3 ยฟ ยฟ ๐ป๐๐ 25 5 ๐๐๐ 30 15 ยฟ ยฟ ๐ป๐๐ 34 17 ๐ด๐ท๐ฝ 48 24 ยฟ ยฟ ๐ป๐๐ 50 25
5 Question Wrap-Up 1. The Pythagorean Theorem helps you solve for a missing of a triangle. 2. We apply the Pythagorean Theorem to triangles. 3. Simplify 4. Write the acronym used to trigonometric functions. 5. The only trig function that doesnโt use the hypotenuse is the function.
UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3.2 Finding Sides and Angles of Right Triangles
Daily 3.2 Missing Sides and Ang functions Agenda angle output input
Daily 3.2 Missing Sides and Ang Agenda x x ๐๐๐ sin ๐ ๐ป๐๐ sin 19 ๐ฅ 11 11 sin 19 ๐ฅ 3.58 ๐ฅ x ๐ด๐ท๐ฝ ๐๐๐ cos ๐ถ sin ๐ป ๐ป๐๐ ๐ป๐๐ 19.2 11 cos 46 sin 34 ๐ฅ ๐ฅ 19.2 11 ๐ฅ ๐ฅ cos 46 sin 34 ๐ฅ 27.64 ๐ฅ 19.67
Daily 3.2 Missing Sides and Ang Check for Understanding Agenda x tan26 ๐๐๐ ๐ด๐ท๐ฝ 14.63 ๐ฅ tan50 ๐๐๐ ๐ด๐ท๐ฝ ๐ฅ 15.49 ๐๐๐ tan20 ๐ด๐ท๐ฝ ๐ฅ 6.92
Daily 3.2 Missing Sides and Ang Agenda sin cos tan -1 -1 -1 Example 2 ๐ก๐๐ ๐ฅ 5 5 ๐ก๐๐ ๐ฅ 1 tan 1 (1 ) ๐ฅ ๐ก๐๐ ๐ฅ tan 1 5 12 5 ๐ฅ 12 ( ) 45 ๐ฅ 22.6 ๐ฅ ๐๐๐ ๐ฅ cos 1 40 42 40 ๐ฅ 42 ( ) 17.8 ๐ฅ
Daily 3.2 Missing Sides and Ang Example 3 Agenda cos 1 15 ๐ฅ 28 ( ) 57.6 ๐ฅ sin 1 19 ๐ฅ 23 ( ) 55.7 ๐ฅ cos 1 70 ๐ฅ 86 ( ) 35.5 ๐ฅ
5 Question Wrap-Up 1. The side across from the discussed angle is called/labeled . 2. Simplify Show full break-down work. 3. Inverse trig functions help solve for missing . 4. Solve for x.
UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3.3 Sine and Cosine of Complementary Angles
3.3 Sine and Cosine of Complementary An Daily What am I learning Agenda 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 Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door opposite angle cosine
3.3 Sine and Cosine of Complementary An Daily What am I learning Agenda 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 ยฟ๐๐จ๐ฌ๐๐ ยฟ๐ฌ๐ข๐ง ๐ ยฟ๐ฌ๐ข๐ง ๐๐ ยฟ๐๐จ๐ฌ๐๐ ยฟ๐ฌ๐ข๐ง๐๐ ยฟ๐๐จ๐ฌ ๐๐ Check for Understanding How will I show you that Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door ยฟ๐๐จ๐ฌ๐๐ ยฟ๐ฌ๐ข๐ง ๐๐ ยฟ๐ฌ๐ข๐ง๐๐ ยฟ๐๐จ๐ฌ๐๐ ยฟ๐ฌ๐ข๐ง ๐๐ ยฟ๐๐จ๐ฌ๐๐
3.3 Sine and Cosine of Complementary An Daily Example 2 What am I learning Agenda 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 Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐
3.3 Sine and Cosine of Complementary An Daily Example 2 continued What am I learning Agenda 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 Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door ๐.๐ ๐.๐๐๐ ๐.๐๐๐ ๐ .๐ Sin A and Cos B are the same which means the complement of sine and cosi equal.
3.3 Sine and Cosine of Complementary An Daily Example 3 What am I learning Agenda today? G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? ๐ . ๐๐๐ ๐๐จ๐ฌ๐๐ Find the complement of sine and cosine How will I show you that Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door ๐ฌ๐ข๐ง ๐๐ ๐ . ๐
3.3 Sine and Cosine of Complementary An Daily What am I learning Example 4 Agenda 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 ๐ ๐๐ ๐ ๐๐ How will I show you that Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door ๐๐ ๐๐ ๐๐ ๐๐ A 13 52 122 ๐ฅ2 5 2 5 144 ๐ฅ 2 13 1 69 ๐ฅ 2 13 ๐ฅ C 12 B A 37 122 35 2 ๐ฅ2 2 1 44 1225 ๐ฅ 1 369 ๐ฅ 2 37 ๐ฅ 35 H 37 12 T
3.3 Sine and Cosine of Complementary An Daily What am I learning Check for Understanding Agenda 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 Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door 10 ๐ ๐ ๐ ๐ 8 2 62 ๐ฅ 2 6 4 36 ๐ฅ 2 1 00 ๐ฅ 2 10 ๐ฅ T.O.T.D. Slide
UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3.4 Application of Trig
3.4 Solve Right Triangles using Daily Trigonometric Ratios What am I learning Agenda 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 Iโve 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 Trigonometric Ratios What am I learning Agenda 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 Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door 9.4 2 9. 4 19 71 3.12 8.9 2 ๐ฅ 2 9 .61 79.21 ๐ฅ 2 8 8.82 ๐ฅ 2 9.42 ๐ฅ tan 1 3.1 ๐ 8.9 ( ) 19.2 ๐ R 90 โ 19.2 70.8
3.4 Solve Right Triangles using Daily Trigonometric Ratios What am I learning Agenda 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 Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door Example 2 sin 32 3.9 2 6.27 3.9 2 6.27 58 ๐ต๐ถ 7.4 3.92 ๐ต๐ถ ๐ฅ2 3.9 2 7.4 2 ๐ฅ2 15.21 54.76 ๐ฅ2 39.55 ๐ฅ 6.27 C 90 โ 32 58
3.4 Solve Right Triangles using Daily Trigonometric Ratios What am I learning Agenda 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 Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door angle of elevation angle of depression
3.4 Solve Right Triangles using Daily Trigonometric Ratios What am I learning Agenda 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 Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door Example 3
3.4 Solve Right Triangles using Daily Trigonometric Ratios What am I learning Agenda 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 Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door Check for Understanding
3.4 Solve Right Triangles using Daily Trigonometric Ratios What am I learning Agenda today? G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? Example 4 Use the Pythagorean Theorem to Solve Right Triangles Use Trigonometric Ratios to Solve Right Triangles How will I show you that Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door 618.75 ft
3.4 Solve Right Triangles using Daily Trigonometric Ratios What am I learning Agenda today? G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? Example 5 Use the Pythagorean Theorem to Solve Right Triangles Use Trigonometric Ratios to Solve Right Triangles How will I show you that Iโve learned it? 5 Question Daily Assessment Daily Ticket out the Door 991.86 ft
