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Angle of Elevation
        and Slope
Slope              Tangent

rise                   opp

             run                adj
               rise            opposite
       slope =           tan =
               run             adjacent
Angle of Elevation
                     Angle of elevation
Example
Stacey needed to shingle her roof. The roofer asked her for the angle of elevation
of her roof. Help Stacey calculate the angle.




                                              5 ft


                                                              14 ft
Example
Stacey needed to shingle her roof. The roofer asked her for the angle of elevation
of her roof. Help Stacey calculate the angle.




                                                                     5 ft

                                                                                     x

                                                                             14 ft
Example
Stacey needed to shingle her roof. The roofer asked her for the angle of elevation
of her roof. Help Stacey calculate the angle.




                                                                     5 ft

                                                                                     x

                                                                             14 ft
Example
Stacey needed to shingle her roof. The roofer asked her for the angle of elevation
of her roof. Help Stacey calculate the angle.




                                                                     5 ft

                                                                                     x

                                                                             14 ft
Example
Stacey needed to shingle her roof. The roofer asked her for the angle of elevation
of her roof. Help Stacey calculate the angle.




                                                                     5 ft

                                                                                     x

                                                                             14 ft
Example
Stacey needed to shingle her roof. The roofer asked her for the angle of elevation
of her roof. Help Stacey calculate the angle.




                                                                     5 ft

                                                                                     x

                                                                             14 ft
Example
Stacey needed to shingle her roof. The roofer asked her for the angle of elevation
of her roof. Help Stacey calculate the angle.




                                                                     5 ft

                                                                                      x

                                                                             14 ft

                                The angle of elevation of Stacey’s roof is 19.65°.
Example
A control tower operator is looking at a plane taking off. If he can see the plane at
an angle of elevation of 15° and the plane is 350 m above the control tower, what
is the horizontal distance from the control tower to the airplane?




                    15°
                                                                                        350 m
Example
A control tower operator is looking at a plane taking off. If he can see the plane at
an angle of elevation of 15° and the plane is 350m above the control tower, what
is the horizontal distance from the control tower to the airplane?




                                                  15°                                   350 m
Example
A control tower operator is looking at a plane taking off. If he can see the plane at
an angle of elevation of 15° and the plane is 350m above the control tower, what
is the horizontal distance from the control tower to the airplane?




                                                  15°                                   350 m
Example
A control tower operator is looking at a plane taking off. If he can see the plane at
an angle of elevation of 15° and the plane is 350m above the control tower, what
is the horizontal distance from the control tower to the airplane?




                                                  15°                                   350 m
Example
A control tower operator is looking at a plane taking off. If he can see the plane at
an angle of elevation of 15° and the plane is 350m above the control tower, what
is the horizontal distance from the control tower to the airplane?




                                                  15°                                   350 m
Example
A control tower operator is looking at a plane taking off. If he can see the plane at
an angle of elevation of 15° and the plane is 350m above the control tower, what
is the horizontal distance from the control tower to the airplane?




                                                  15°                                   350 m
Example
A control tower operator is looking at a plane taking off. If he can see the plane at
an angle of elevation of 15° and the plane is 350m above the control tower, what
is the horizontal distance from the control tower to the airplane?




                                                  15°                                   350 m
Example
A control tower operator is looking at a plane taking off. If he can see the plane at
an angle of elevation of 15° and the plane is 350m above the control tower, what
is the horizontal distance from the control tower to the airplane?




                                                  15°                                   350 m
Example
A control tower operator is looking at a plane taking off. If he can see the plane at
an angle of elevation of 15° and the plane is 350m above the control tower, what
is the horizontal distance from the control tower to the airplane?




                                                  15°                                   350 m
Example
A control tower operator is looking at a plane taking off. If he can see the plane at
an angle of elevation of 15° and the plane is 350m above the control tower, what
is the horizontal distance from the control tower to the airplane?




                                                  15°                                   350 m




                               The plane is 1306 m away from the control tower.
Summary
Finding angle of elevation       Finding a side using angle of elevation




                             x
IMAGE CREDITS
  Bow Valley College

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Mat2793 - Angle of Elevation

  • 1. Angle of Elevation and Slope
  • 2. Slope Tangent rise opp run adj rise opposite slope = tan = run adjacent
  • 3. Angle of Elevation Angle of elevation
  • 4. Example Stacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle. 5 ft 14 ft
  • 5. Example Stacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle. 5 ft x 14 ft
  • 6. Example Stacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle. 5 ft x 14 ft
  • 7. Example Stacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle. 5 ft x 14 ft
  • 8. Example Stacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle. 5 ft x 14 ft
  • 9. Example Stacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle. 5 ft x 14 ft
  • 10. Example Stacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle. 5 ft x 14 ft  The angle of elevation of Stacey’s roof is 19.65°.
  • 11. Example A control tower operator is looking at a plane taking off. If he can see the plane at an angle of elevation of 15° and the plane is 350 m above the control tower, what is the horizontal distance from the control tower to the airplane? 15° 350 m
  • 12. Example A control tower operator is looking at a plane taking off. If he can see the plane at an angle of elevation of 15° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane? 15° 350 m
  • 13. Example A control tower operator is looking at a plane taking off. If he can see the plane at an angle of elevation of 15° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane? 15° 350 m
  • 14. Example A control tower operator is looking at a plane taking off. If he can see the plane at an angle of elevation of 15° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane? 15° 350 m
  • 15. Example A control tower operator is looking at a plane taking off. If he can see the plane at an angle of elevation of 15° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane? 15° 350 m
  • 16. Example A control tower operator is looking at a plane taking off. If he can see the plane at an angle of elevation of 15° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane? 15° 350 m
  • 17. Example A control tower operator is looking at a plane taking off. If he can see the plane at an angle of elevation of 15° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane? 15° 350 m
  • 18. Example A control tower operator is looking at a plane taking off. If he can see the plane at an angle of elevation of 15° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane? 15° 350 m
  • 19. Example A control tower operator is looking at a plane taking off. If he can see the plane at an angle of elevation of 15° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane? 15° 350 m
  • 20. Example A control tower operator is looking at a plane taking off. If he can see the plane at an angle of elevation of 15° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane? 15° 350 m  The plane is 1306 m away from the control tower.
  • 21. Summary Finding angle of elevation Finding a side using angle of elevation x
  • 22. IMAGE CREDITS Bow Valley College

Notas del editor

  1. (section 6.5)PurposeTo demonstrate how to find angle of elevationand using rise and run, how to solve angle of elevation questions to find rise or run
  2. Review previous topic: slope is rise over run, tangent is opposite over adjacent. We are assuming that students have worked with slope earlier in the unit and tangent in a previous unit.
  3. This slide is to show how the angle of elevation is related to the slope. We have used an image of a house with a roof to show the rise and run of the roof and the angle is between the horizontal line (run) and the hypotenuse.
  4. The triangle will highlight the information needed to solve this example. The rise and run are labeled.
  5. Only the roof of the house is shown with all known and unknown dimensions labeled. Introduce formulaFill in formulaRearrange formulaFind answer with answer statement
  6. Only the roof of the house is shown with all known and unknown dimensions labeled. Introduce formulaFill in formulaRearrange formulaFind answer with answer statement
  7. Only the roof of the house is shown with all known and unknown dimensions labeled. Introduce formulaFill in formulaRearrange formulaFind answer with answer statement
  8. Only the roof of the house is shown with all known and unknown dimensions labeled. Introduce formulaFill in formulaRearrange formulaFind answer with answer statement
  9. Only the roof of the house is shown with all known and unknown dimensions labeled. Introduce formulaFill in formulaRearrange formulaFind answer with answer statement
  10. Only the roof of the house is shown with all known and unknown dimensions labeled. Introduce formulaFill in formulaRearrange formulaFind answer with answer statement
  11. Introduce example with diagram of airplane and control tower. All dimensions are labeled.
  12. Same diagram but zoomed out.Identify all parts involved, and show what you know and what you are looking for (have 2 pieces still and need to find the third)Introduce formula.Fill in formula. Rearrange formula. Find answer with answer statement.
  13. Same diagram but zoomed out.Identify all parts involved, and show what you know and what you are looking for (have 2 pieces still and need to find the third)Introduce formula.Fill in formula. Rearrange formula. Find answer with answer statement.
  14. Same diagram but zoomed out.Identify all parts involved, and show what you know and what you are looking for (have 2 pieces still and need to find the third)Introduce formula.Fill in formula. Rearrange formula. Find answer with answer statement.
  15. Same diagram but zoomed out.Identify all parts involved, and show what you know and what you are looking for (have 2 pieces still and need to find the third)Introduce formula.Fill in formula. Rearrange formula. Find answer with answer statement.
  16. Same diagram but zoomed out.Identify all parts involved, and show what you know and what you are looking for (have 2 pieces still and need to find the third)Introduce formula.Fill in formula. Rearrange formula. Find answer with answer statement.
  17. Same diagram but zoomed out.Identify all parts involved, and show what you know and what you are looking for (have 2 pieces still and need to find the third)Introduce formula.Fill in formula. Rearrange formula. Find answer with answer statement.
  18. Same diagram but zoomed out.Identify all parts involved, and show what you know and what you are looking for (have 2 pieces still and need to find the third)Introduce formula.Fill in formula. Rearrange formula. Find answer with answer statement.
  19. Same diagram but zoomed out.Identify all parts involved, and show what you know and what you are looking for (have 2 pieces still and need to find the third)Introduce formula.Fill in formula. Rearrange formula. Find answer with answer statement.
  20. Same diagram but zoomed out.Identify all parts involved, and show what you know and what you are looking for (have 2 pieces still and need to find the third)Introduce formula.Fill in formula. Rearrange formula. Find answer with answer statement.
  21. Summary of the 2 examples and what you were looking for in each one and which equations you would use.