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Today – Monday, March 11, 2013 Review for QUIZ QUIZ Learning Target : Use Trigonometry and Inverse Trig to find missing sides and angles of a triangle Independent Practice

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**Finding missing angles using INVERSE TRIG**

REVIEW FOR QUIZ: Finding missing sides of a right triangle using SPECIAL RIGHT TRIANGLES and TRIG Finding missing angles using INVERSE TRIG

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**Use the Pythagorean Theorem**

WARM UP: Find the missing sides for the following triangles. 𝑥 30° 17 𝑥 𝑦 𝑥 14 20 45° 𝑦 11 Use the Pythagorean Theorem 𝑙𝑒𝑔 2 + 𝑙𝑒𝑔 2 = ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 2 = 𝑥 2 = 𝑥 2 317= 𝑥 2 317 = 𝑥 2 𝟑𝟏𝟕 =𝒙 Use 𝟑𝟎°−𝟔𝟎°−𝟗𝟎° Triangle ℎ𝑦𝑝𝑜𝑛𝑡𝑒𝑛𝑢𝑠𝑒=2·𝑠ℎ𝑜𝑟𝑡 𝑙𝑒𝑔 20=2·𝑦 𝟏𝟎=𝒚 𝑙𝑜𝑛𝑔 𝑙𝑒𝑔=𝑠ℎ𝑜𝑟𝑡 𝑙𝑒𝑔· 3 𝒙=𝟏𝟎 𝟑 Use 𝟒𝟓°−𝟒𝟓°−𝟗𝟎° Triangle ℎ𝑦𝑝𝑜𝑛𝑡𝑒𝑛𝑢𝑠𝑒=𝑙𝑒𝑔· 2 17=𝑥· 2 =𝑥 · = 𝒙= 𝟏𝟕 𝟐 𝟐 𝒚= 𝟏𝟕 𝟐 𝟐

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**67 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 46° 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒 𝑦 𝑥 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒**

PRACTICE: Find x and y using the tangent ratio. Round answer to the nearest tenth. 67 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 46° 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒 𝑦 𝑥 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒 Solve for x using 𝒔𝒊𝒏𝜽= 𝑶 𝑯 𝑠𝑖𝑛46°= 𝑥 67 67·𝑠𝑖𝑛46°= 𝑥 67 ·67 67𝑠𝑖𝑛46°=𝑥 𝟒𝟖.𝟐=𝒙 Solve for y using 𝒄𝒐𝒔𝜽= 𝑨 𝑯 𝑐𝑜𝑠46°= 𝑦 67 67·𝑐𝑜𝑠46°= 𝑦 67 ·67 67𝑐𝑜𝑠46°=𝑦 𝒚=𝟒𝟔.𝟓

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**𝑥 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒 52 26° 𝑦 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒**

PRACTICE: Find x and y using the tangent ratio. Round answer to the nearest tenth. 𝑥 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒 52 26° 𝑦 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒 Solve for x using 𝒔𝒊𝒏𝜽= 𝑶 𝑯 𝑠𝑖𝑛26°= 52 𝑥 Variable is on the bottom of the ratio so…divide! 𝑥= 52 𝑠𝑖𝑛26° 𝒙=𝟐𝟐.𝟖 Solve for y using 𝒕𝒂𝒏𝜽= 𝑶 𝑨 𝑡𝑎𝑛26°= 52 𝑦 Variable is on the bottom of the ratio so…divide! 𝑥= 52 𝑡𝑎𝑛26° 𝒚=𝟐𝟓.𝟒

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**𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒 14 𝑥 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒 13**

PRACTICE: Find angle x using inverse trigonometric functions. Round your answer to the nearest hundredth. 14 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒 𝑥 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒 13 Use tangent ratio 𝑡𝑎𝑛𝑥= 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 = 𝑂 𝐴 Substitute known values 𝑡𝑎𝑛𝑥= 14 13 Use inverse tangent 𝑥= 𝑡𝑎𝑛 − Solve for x using calculator 𝒙=𝟒𝟕.𝟏𝟐°

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**𝑥 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 36 24 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒**

PRACTICE: Find angle x using inverse trigonometric functions. Round your answer to the nearest hundredth. 𝑥 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 36 24 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒 Use cosine ratio 𝑐𝑜𝑠𝜃= 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 𝐴 𝐻 Substitute known values 𝑐𝑜𝑠𝑥= 24 36 Use inverse cosine 𝑥= 𝑐𝑜𝑠 − Solve for x using calculator 𝒙=𝟒𝟖.𝟏𝟐

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**CHAPTER 7.4-7.6 QUIZ You have the rest of class to complete your quiz**

Are you prepared? Pencil? Calculator? Chapter 7 notes ONLY allowed If you finish early: Finish any missing assignments. Work on something quietly as the rest of your fellow classmates complete their quizzes. NO TALKING. STAY IN YOUR SEATS. RETURN ANY BORROWED BOOKS & CALCULATORS

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**HOMEWORK #8: Angles of Elevation and Depression WS#2**

If finished, work on other assignments: HW #1: Pg. 436: 3-29 odd HW #2: Pg. 444: 1-6, 8, 10, 12 HW #3: Pg. 461: 3-18 HW #4: 7.4 Special Triangles WS (Kuta) HW #5: Pg. 470: 18-20, 24-29, 31, 32 Pg. 477: 10-15, 18-27 HW #6: Pg. 485: 3-8, 10-18 HW #7: Angles of Elevation and Depression WS #1

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