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Mat2793 - Angle of Elevation

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Angle of Elevation and Slope
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Page 1: Mat2793 - Angle of Elevation

Angle of Elevation and Slope

Page 2: Mat2793 - Angle of Elevation

Slope

rise

run

rise run

slope =

adj

opposite adjacenttan =

opp

Tangent

Page 3: Mat2793 - Angle of Elevation

Angle of ElevationAngle of elevation

Page 4: Mat2793 - Angle 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

Page 5: Mat2793 - Angle 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

tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛

x

5 ft

Page 6: Mat2793 - Angle 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

tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛

tan𝑥=514

x

5 ft

Page 7: Mat2793 - Angle 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

tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛

tan𝑥=514

tan−1 tan 𝑥=tan− 1514

x

5 ft

Page 8: Mat2793 - Angle 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

tan𝑥=𝑟𝑖𝑠𝑒𝑟𝑢𝑛

tan𝑥=514

tan−1 tan 𝑥=tan− 1514

𝑥=tan−1514

x

5 ft

Page 9: Mat2793 - Angle 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

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

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

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

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

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

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

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

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

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

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

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

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

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

IMAGE CREDITSBow Valley College


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