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UNIT 3: RIGHT TRIANGLE TRIGONOMETRY Vocabulary Builder Similar Triangles leg Pythagorean Theorem Square Root Simplest radical form 45-45-90 Triangles Hypotenuse Variable 30-60-90 Triangles UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3.1 Trigonometric Ratios Square root Perfect Square Radical expression radicand Perfect Square 5 8 14 30 18 π π 2 π 3 ππ 10 π 3 ππ π π 23 right triangle equals hypotenuse Side lengths 42 + 82 = π₯2 16 + 64 = π₯ 80 = 2 π₯2 62 + 32 = π₯2 π₯ 2 + 3.92 = 112 2 π₯ 2 + 15.21 = 121 36 + 9 = π₯ 45 = π₯2 4 5=π₯ 3 5=π₯ 8.9 = π₯ 6.7 = π₯ π₯ 2 = 95.79 π₯ = 9.75 32 + 102 = π₯2 9 + 100 = π₯2 109 = π₯2 10.44 = π₯ 72 + 22 = π₯2 π₯ 2 + 3.62 = 7.42 2 π₯ 2 + 12.96 = 54.76 49 + 4 = π₯ π₯2 π₯ 2 = 41.8 7.3 = π₯ π₯ = 6.47 53 = hypotenuse adjacent opposite ππ ππ ππ π»π ππΌ π»πΌ trigonometric ratio SOH CAH TOA right length acute SOH CAH TOA 4 πππ 20 = = 3 π΄π·π½ 15 πππ 16 8 = = π΄π·π½ 30 15 7 πππ 14 = = π΄π·π½ 48 24 πππ 15 3 = = π»ππ 25 5 πππ 30 15 = = π»ππ 34 17 π΄π·π½ 48 24 = = π»ππ 50 25 = 11 29 25 = 11 = 11 29 18 = 7 = 25 29 =1 UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3.2 Finding Sides and Angles of Right Triangles function angle output input x x x sin π = πππ π»ππ π₯ sin 19° = 11 11 β sin 19° = π₯ 3.58 = π₯ cos πΆ = π΄π·π½ π»ππ 19.2 cos 46° = π₯ 19.2 π₯= cos 46° π₯ = 27.64 sin π» = πππ π»ππ 11 sin 34° = π₯ 11 π₯= sin 34° π₯ = 19.67 x tan 26° = πππ π΄π·π½ 14.63 = π₯ π΄π·π½ π»ππ πππ tan 20° = π΄π·π½ π₯ = 15.49 π₯ = 6.92 tan 50° = sin-1 cos-1 tan-1 5 5 tanβ1 π₯ = 1 tanβ1 π₯ = tanβ1 1 = π₯ 45° = π₯ tanβ1 π₯ = tanβ1 5 12 5 =π₯ 12 22.6° = π₯ cos β1 π₯ = cos β1 40 42 20 =π₯ 21 17.8° = π₯ cos β1 15 =π₯ 28 57.6° = π₯ sinβ1 19 =π₯ 23 55.7° = π₯ cos β1 35 =π₯ 43 35.5° = π₯ UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3.3 Sine and Cosine of Complementary Angles What am I learning today? β’G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles 180Λ 90Λ complementary What am I going to do today? β’Find the complement of sine and cosine How will I show you that Iβve learned it? β’5 Question Daily Assessment β’Daily Ticket out the Door Opposite angle cosine What am I learning today? β’G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? = ππ¨π¬ ππ° = ππ¨π¬ ππ° = π¬π’π§ π° = π¬π’π§ ππ° = π¬π’π§ ππ° = ππ¨π¬ ππ° β’Find the complement of sine and cosine How will I show you that Iβve learned it? β’5 Question Daily Assessment β’Daily Ticket out the Door = ππ¨π¬ ππ° = π¬π’π§ ππ° = π¬π’π§ ππ° = ππ¨π¬ ππ° = π¬π’π§ ππ° = ππ¨π¬ ππ° What am I learning today? β’G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? β’Find the complement of sine and cosine How will I show you that Iβve learned it? β’5 Question Daily Assessment β’Daily Ticket out the Door π π π π π π π π Sin A and Cos B are the same which means The complement of sine and cosine are equal. What am I learning today? β’G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles Then mοQ = 60Λ What am I going to do today? β’Find the complement of sine and cosine How will I show you that Iβve learned it? β’5 Question Daily Assessment β’Daily Ticket out the Door π. π π. πππ π. πππ π. π The complement of sine and cosine are equal. What am I learning today? 102 + 242 = π₯ 2 β’G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles Then mοT = 45Λ 100 + 576 = π₯ 2 676 = π₯ 2 26 = π₯ 26 What am I going to do today? β’Find the complement of sine and cosine How will I show you that Iβve learned it? β’5 Question Daily Assessment β’Daily Ticket out the Door ππ ππ = ππ ππ ππ π = ππ ππ π. πππ π. πππ ππ π = ππ ππ ππ ππ = ππ ππ π. πππ π. πππ The complement of sine and cosine are equal. What am I learning today? β’G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles ππ¨π¬ ππ° β π. πππ What am I going to do today? β’Find the complement of sine and cosine How will I show you that Iβve learned it? β’5 Question Daily Assessment β’Daily Ticket out the Door π¬π’π§ ππ° β π. π What am I learning today? β’G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? β’Find the complement of sine and cosine π ππ π ππ How will I show you that Iβve learned it? β’5 Question Daily Assessment β’Daily Ticket out the Door A 13 52 + 122 = π₯ 2 5 25 + 144 = π₯ 2 169 = π₯ 2 13 = π₯ C 12 B A 37 ππ ππ ππ ππ 13 122 + 352 = π₯ 2 144 + 1225 = π₯ 35 2 1369 = π₯ 2 37 = π₯ H 37 12 T What am I learning today? β’G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? β’Find the complement of sine and cosine 10 π π π π How will I show you that Iβve learned it? β’5 Question Daily Assessment β’Daily Ticket out the Door X 82 + 62 = π₯ 2 64 + 36 = π₯ 2 100 = π₯ 2 10 = π₯ 10 π π π π 10 8 Y Z 6 X 32 + π₯ 2 = 52 9 + π₯ 2 = 25 5 3 π₯ 2 = 16 π₯=4 I 4 M What am I learning today? β’G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? β’Find the complement of sine and cosine How will I show you that Iβve learned it? β’5 Question Daily Assessment β’Daily Ticket out the Door What am I learning today? β’G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles What am I going to do today? β’Find the complement of sine and cosine How will I show you that Iβve learned it? β’5 Question Daily Assessment β’Daily Ticket out the Door UNIT 3: RIGHT TRIANGLE TRIGONOMETRY 3.4 Solve Right Triangles What am I learning today? β’G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? β’Use the Pythagorean Theorem to Solve Right Triangles β’Use Trigonometric Ratios to Solve Right Triangles How will I show you that Iβve learned it? β’ 5 Question Daily Assessment β’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 What am I learning today? β’G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? β’Use the Pythagorean Theorem to Solve Right Triangles β’Use Trigonometric Ratios to Solve Right Triangles How will I show you that Iβve learned it? β’ 5 Question Daily Assessment β’Daily Ticket out the Door 9.4 9.4 19.2Λ 70.8Λ 3.12 + 8.92 = π₯ 2 9.61 + 79.21 = π₯ 2 88.82 = π₯ 2 9.4 = π₯ tanβ1 3.1 = β π 8.9 19.2° = β π οR = 90 β 19.2 = 70.8Λ What am I learning today? β’G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? β’Use the Pythagorean Theorem to Solve Right Triangles β’Use Trigonometric Ratios to Solve Right Triangles How will I show you that Iβve learned it? β’ 5 Question Daily Assessment β’Daily Ticket out the Door 3.9 6.3 3.9 6.3Λ 58Λ π΅πΆ sin 32° = 7.4 3.58 = π₯ π₯ 2 + 3.92 = 7.42 π₯ 2 + 15.21 = 54.76 π₯ 2 = 39.55 π₯ = 6.3 οC = 90 β 32 = 58Λ What am I learning today? β’G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? β’Use the Pythagorean Theorem to Solve Right Triangles β’Use Trigonometric Ratios to Solve Right Triangles How will I show you that Iβve learned it? β’ 5 Question Daily Assessment β’Daily Ticket out the Door Angle of Elevation Angle of Depression What am I learning today? β’G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? β’Use the Pythagorean Theorem to Solve Right Triangles β’Use Trigonometric Ratios to Solve Right Triangles How will I show you that Iβve learned it? β’ 5 Question Daily Assessment β’Daily Ticket out the Door What am I learning today? β’G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? β’Use the Pythagorean Theorem to Solve Right Triangles β’Use Trigonometric Ratios to Solve Right Triangles How will I show you that Iβve learned it? β’ 5 Question Daily Assessment β’Daily Ticket out the Door What am I learning today? β’G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? β’Use the Pythagorean Theorem to Solve Right Triangles β’Use Trigonometric Ratios to Solve Right Triangles How will I show you that Iβve learned it? β’ 5 Question Daily Assessment β’Daily Ticket out the Door 618.75 ft2 What am I learning today? β’G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? β’Use the Pythagorean Theorem to Solve Right Triangles β’Use Trigonometric Ratios to Solve Right Triangles How will I show you that Iβve learned it? β’ 5 Question Daily Assessment β’Daily Ticket out the Door 991.86 ft2 What am I learning today? β’G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? β’Use the Pythagorean Theorem to Solve Right Triangles β’Use Trigonometric Ratios to Solve Right Triangles How will I show you that Iβve learned it? β’ 5 Question Daily Assessment β’Daily Ticket out the Door What am I learning today? β’G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve triangles in applied problems What am I going to do today? β’Use the Pythagorean Theorem to Solve Right Triangles β’Use Trigonometric Ratios to Solve Right Triangles How will I show you that Iβve learned it? β’ 5 Question Daily Assessment β’Daily Ticket out the Door