Date post: | 01-Dec-2014 |
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Education |
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Angle of Elevation and Slope
Slope
rise
run
rise run
slope =
adj
opposite adjacenttan =
opp
Tangent
Angle of ElevationAngle of elevation
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
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
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
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
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
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
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°.
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
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
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
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
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
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
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
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
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
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
Finding angle of elevation Finding a side using angle of elevation
x
Summary
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
𝑟𝑢𝑛=𝑟𝑖𝑠𝑒tan𝑥 𝑟𝑖𝑠𝑒=𝑟𝑢𝑛 ∙ tan 𝑥
IMAGE CREDITSBow Valley College