1. 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

2. 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

3. 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

4. 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

5. 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

6. 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°

7. 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

8. 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

9. 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