Mat2793 - Angle of Elevation

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  • (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
  • 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.
  • 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.
  • The triangle will highlight the information needed to solve this example. The rise and run are labeled.
  • Only the roof of the house is shown with all known and unknown dimensions labeled. Introduce formulaFill in formulaRearrange formulaFind answer with answer statement
  • Only the roof of the house is shown with all known and unknown dimensions labeled. Introduce formulaFill in formulaRearrange formulaFind answer with answer statement
  • Only the roof of the house is shown with all known and unknown dimensions labeled. Introduce formulaFill in formulaRearrange formulaFind answer with answer statement
  • Only the roof of the house is shown with all known and unknown dimensions labeled. Introduce formulaFill in formulaRearrange formulaFind answer with answer statement
  • Only the roof of the house is shown with all known and unknown dimensions labeled. Introduce formulaFill in formulaRearrange formulaFind answer with answer statement
  • Only the roof of the house is shown with all known and unknown dimensions labeled. Introduce formulaFill in formulaRearrange formulaFind answer with answer statement
  • Introduce example with diagram of airplane and control tower. All dimensions are labeled.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Summary of the 2 examples and what you were looking for in each one and which equations you would use.
  • Mat2793 - Angle of Elevation

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

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