mat2793 - angle of elevation
DESCRIPTION
TRANSCRIPT
![Page 1: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/1.jpg)
Angle of Elevation and Slope
![Page 2: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/2.jpg)
Slope
rise
run
rise run
slope =
adj
opposite adjacenttan =
opp
Tangent
![Page 3: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/3.jpg)
Angle of ElevationAngle of elevation
![Page 4: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/4.jpg)
ExampleStacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle.
14 ft
5 ft
![Page 5: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/5.jpg)
ExampleStacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle.
14 ft
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
x
5 ft
![Page 6: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/6.jpg)
ExampleStacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle.
14 ft
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan𝑥=514
x
5 ft
![Page 7: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/7.jpg)
ExampleStacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle.
14 ft
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan𝑥=514
tan−1 tan 𝑥=tan− 1514
x
5 ft
![Page 8: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/8.jpg)
ExampleStacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle.
14 ft
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan𝑥=514
tan−1 tan 𝑥=tan− 1514
𝑥=tan−1514
x
5 ft
![Page 9: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/9.jpg)
ExampleStacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle.
14 ft
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan𝑥=514
tan−1 tan 𝑥=tan− 1514
𝑥=tan−1514
𝑥=19.65 °
x
5 ft
![Page 10: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/10.jpg)
ExampleStacey needed to shingle her roof. The roofer asked her for the angle of elevation of her roof. Help Stacey calculate the angle.
14 ft
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan𝑥=514
tan−1 tan 𝑥=tan− 1514
𝑥=tan−1514
𝑥=19.65 °
x
5 ft
The angle of elevation of Stacey’s roof is 19.65°.
![Page 11: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/11.jpg)
ExampleA 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
𝑥
![Page 12: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/12.jpg)
ExampleA 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?
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
15° 350 m
𝑥
![Page 13: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/13.jpg)
ExampleA 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?
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan 15=350𝑥
15° 350 m
𝑥
![Page 14: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/14.jpg)
ExampleA 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?
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan 15=350𝑥
𝑥 tan 15=𝑥350𝑥
15° 350 m
𝑥
![Page 15: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/15.jpg)
ExampleA 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?
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan 15=350𝑥
𝑥 tan 15=𝑥350𝑥
15° 350 m
𝑥
![Page 16: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/16.jpg)
ExampleA 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?
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan 15=350𝑥
𝑥 tan 15=𝑥350𝑥
𝑥 tan 15=350
15° 350 m
𝑥
![Page 17: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/17.jpg)
ExampleA 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?
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan 15=350𝑥
𝑥 tan 15=𝑥350𝑥
𝑥 tan 15=350
𝑥tan 15tan 15
=350tan 15
15° 350 m
𝑥
![Page 18: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/18.jpg)
ExampleA 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?
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan 15=350𝑥
𝑥 tan 15=𝑥350𝑥
𝑥 tan 15=350
𝑥tan 15tan 15
=350tan 15
15° 350 m
𝑥
![Page 19: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/19.jpg)
ExampleA 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?
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan 15=350𝑥
𝑥 tan 15=𝑥350𝑥
𝑥 tan 15=350
𝑥tan 15tan 15
=350tan 15
𝑥=1306𝑚
15° 350 m
𝑥
![Page 20: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/20.jpg)
ExampleA 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?
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan 15=350𝑥
𝑥 tan 15=𝑥350𝑥
𝑥 tan 15=350
𝑥tan 15tan 15
=350tan 15
𝑥=1306𝑚 The plane is 1306 m away from the control tower.
15° 350 m
𝑥
![Page 21: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/21.jpg)
Finding angle of elevation Finding a side using angle of elevation
x
Summary
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
𝑟𝑢𝑛=𝑟𝑖𝑠𝑒tan𝑥 𝑟𝑖𝑠𝑒=𝑟𝑢𝑛 ∙ tan 𝑥
![Page 22: Mat2793 - Angle of Elevation](https://reader033.vdocuments.site/reader033/viewer/2022061204/547eca0eb4795989508b4c54/html5/thumbnails/22.jpg)
IMAGE CREDITSBow Valley College