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8-5 Trig Angles of Elev and Depress.ppt

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This document defines and provides examples of angles of elevation and depression. It discusses how these angles are formed when viewing an object from a higher or lower position and must have one horizontal side. Several word problems are worked out using trigonometric functions like sine, tangent, and inverse tangent to calculate unknown distances and heights based on a given angle of elevation or depression and one known side length.

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ANGLES OF ELEVATION AND DEPRESSION Jim Smith JCHS Section 8-5 spi.3.1.B
Angles Of Elevation And Depression Must Have One Horizontal Side. Elevation Depression
A B C ACB Is An Angle Of Elevation. DBC Is An Angle Of Depression. ABC Is Not An Angle Of Depression! D
Name The Angles Of Elevation And Depression 1 2 3 4 5 6 Depression Elevation Elevation Depression
Depression Elevation These Angles Are Alternate Interior Angles¡­ They¡¯re Congruent
A Skydiver Jumps From A Plane. When He Lands, The Angle Of Elevation From The Ground To The Plane Is 51¡ã. If The Plane Maintains An Altitude Of 4000 Feet , What Is The Straight Line Distance From The Skydiver To The Plane? 4000 51¡ã X
3 . 5147 4000 7771 . 4000 1 7771 . 4000 51 sin ? ? ? ? x x x x
A Tree Casts A Shadow 87 Feet Long. If The Angle Of Elevation From The Ground To The Top Of The Tree Is 50¡ã, Find The Height Of The Tree. 50¡ã 87 x
feet 7 . 103 87 1 1917 . 1 87 50 tan ? ? ? x x x
If The Kite Is 100 Feet High And The Angle Of Depression From The Kite To Wiley Is 39¡ã, If Wiley Is Holding The String 4 Feet Off The Ground, Find The Distance Along The String The Lightening Must Travel To Reach The Key. 4 96 39 x 39
feet 6 . 156 4 6 . 152 6 . 152 96 1 6293 . 96 39 sin ? ? ? ? ? x x x
A rocket ship is two miles above sea level when it begins to climb at a constant angle of 3.5¡ã for the next 40 ground miles. About how far above sea level is the rocket ship after its climb? 3.5¡ã 40 x 2
Two horses are observed by a hang glider 80 meters above a meadow. The angles of depression are 10.4¡ã and 8¡ã. How far apart are the horses? 8? 10.4? 80 8? 10.4?
Two horses are observed by a hang glider 80 meters above a meadow. The angles of depression are 10.4¡ã and 8¡ã. How far apart are the horses? 8? 80 8? Tan 8¡ã = 80/x X = 569.2 x
Two horses are observed by a hang glider 80 meters above a meadow. The angles of depression are 10.4¡ã and 8¡ã. How far apart are the horses? 10.4? 80 10.4? y Tan 10.4 = 80/y Y = 435.9
Two horses are observed by a hang glider 80 meters above a meadow. The angles of depression are 10.4¡ã and 8¡ã. How far apart are the horses? 80 8? 10.4? 569.2 435.9 569.2 ¨C 435.9 = 133.3
A traffic helicopter pilot 60 meters above the road spotted two cars. The angles of depression are 10.2¡ã and 8.7¡ã. How far apart are the cars?
A traffic helicopter pilot 60 meters above the road spotted two cars. The angles of depression are 10.2¡ã and 8.7¡ã. How far apart are the cars? 8.7¡ã 8.7¡ã 60 Tan 8.7¡ã = 60/x X = 392.1 x
A traffic helicopter pilot 60 meters above the road spotted two cars. The angles of depression are 10.2¡ã and 8.7¡ã. How far apart are the cars? 10.2¡ã 10.2¡ã y Tan 10.2 = 60/y Y = 333.5
A traffic helicopter pilot 60 meters above the road spotted two cars. The angles of depression are 10.2¡ã and 8.7¡ã. How far apart are the cars? 392.1 333.5 392.1 ¨C 333.5 = 58.6

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8-5 Trig Angles of Elev and Depress.ppt

  • 1. ANGLES OF ELEVATION AND DEPRESSION Jim Smith JCHS Section 8-5 spi.3.1.B
  • 2. Angles Of Elevation And Depression Must Have One Horizontal Side. Elevation Depression
  • 3. A B C ACB Is An Angle Of Elevation. DBC Is An Angle Of Depression. ABC Is Not An Angle Of Depression! D
  • 4. Name The Angles Of Elevation And Depression 1 2 3 4 5 6 Depression Elevation Elevation Depression
  • 5. Depression Elevation These Angles Are Alternate Interior Angles¡­ They¡¯re Congruent
  • 6. A Skydiver Jumps From A Plane. When He Lands, The Angle Of Elevation From The Ground To The Plane Is 51¡ã. If The Plane Maintains An Altitude Of 4000 Feet , What Is The Straight Line Distance From The Skydiver To The Plane? 4000 51¡ã X
  • 8. A Tree Casts A Shadow 87 Feet Long. If The Angle Of Elevation From The Ground To The Top Of The Tree Is 50¡ã, Find The Height Of The Tree. 50¡ã 87 x
  • 10. If The Kite Is 100 Feet High And The Angle Of Depression From The Kite To Wiley Is 39¡ã, If Wiley Is Holding The String 4 Feet Off The Ground, Find The Distance Along The String The Lightening Must Travel To Reach The Key. 4 96 39 x 39
  • 12. A rocket ship is two miles above sea level when it begins to climb at a constant angle of 3.5¡ã for the next 40 ground miles. About how far above sea level is the rocket ship after its climb? 3.5¡ã 40 x 2
  • 13. Two horses are observed by a hang glider 80 meters above a meadow. The angles of depression are 10.4¡ã and 8¡ã. How far apart are the horses? 8? 10.4? 80 8? 10.4?
  • 14. Two horses are observed by a hang glider 80 meters above a meadow. The angles of depression are 10.4¡ã and 8¡ã. How far apart are the horses? 8? 80 8? Tan 8¡ã = 80/x X = 569.2 x
  • 15. Two horses are observed by a hang glider 80 meters above a meadow. The angles of depression are 10.4¡ã and 8¡ã. How far apart are the horses? 10.4? 80 10.4? y Tan 10.4 = 80/y Y = 435.9
  • 16. Two horses are observed by a hang glider 80 meters above a meadow. The angles of depression are 10.4¡ã and 8¡ã. How far apart are the horses? 80 8? 10.4? 569.2 435.9 569.2 ¨C 435.9 = 133.3
  • 17. A traffic helicopter pilot 60 meters above the road spotted two cars. The angles of depression are 10.2¡ã and 8.7¡ã. How far apart are the cars?
  • 18. A traffic helicopter pilot 60 meters above the road spotted two cars. The angles of depression are 10.2¡ã and 8.7¡ã. How far apart are the cars? 8.7¡ã 8.7¡ã 60 Tan 8.7¡ã = 60/x X = 392.1 x
  • 19. A traffic helicopter pilot 60 meters above the road spotted two cars. The angles of depression are 10.2¡ã and 8.7¡ã. How far apart are the cars? 10.2¡ã 10.2¡ã y Tan 10.2 = 60/y Y = 333.5
  • 20. A traffic helicopter pilot 60 meters above the road spotted two cars. The angles of depression are 10.2¡ã and 8.7¡ã. How far apart are the cars? 392.1 333.5 392.1 ¨C 333.5 = 58.6