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Angle of Elevation and Slope
22

Mat2793 - Angle of Elevation

Dec 01, 2014

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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

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

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

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tanπ‘₯=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

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tanπ‘₯=514

tanβˆ’1 tan π‘₯=tanβˆ’ 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

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tanπ‘₯=514

tanβˆ’1 tan π‘₯=tanβˆ’ 1514

π‘₯=tanβˆ’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

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tanπ‘₯=514

tanβˆ’1 tan π‘₯=tanβˆ’ 1514

π‘₯=tanβˆ’1514

π‘₯=19.65 Β°

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

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tanπ‘₯=514

tanβˆ’1 tan π‘₯=tanβˆ’ 1514

π‘₯=tanβˆ’1514

π‘₯=19.65 Β°

x

5 ft

The angle of elevation of Stacey’s roof is 19.65Β°.

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 15Β° and the plane is 350 m above the control tower, what is the horizontal distance from the control tower to the airplane?

15Β°350 m

π‘₯

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 15Β° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane?

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

15Β° 350 m

π‘₯

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 15Β° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane?

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tan 15=350π‘₯

15Β° 350 m

π‘₯

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 15Β° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane?

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tan 15=350π‘₯

π‘₯ tan 15=π‘₯350π‘₯

15Β° 350 m

π‘₯

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 15Β° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane?

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tan 15=350π‘₯

π‘₯ tan 15=π‘₯350π‘₯

15Β° 350 m

π‘₯

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 15Β° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane?

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tan 15=350π‘₯

π‘₯ tan 15=π‘₯350π‘₯

π‘₯ tan 15=350

15Β° 350 m

π‘₯

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 15Β° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane?

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tan 15=350π‘₯

π‘₯ tan 15=π‘₯350π‘₯

π‘₯ tan 15=350

π‘₯tan 15tan 15

=350tan 15

15Β° 350 m

π‘₯

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 15Β° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane?

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tan 15=350π‘₯

π‘₯ tan 15=π‘₯350π‘₯

π‘₯ tan 15=350

π‘₯tan 15tan 15

=350tan 15

15Β° 350 m

π‘₯

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 15Β° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane?

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tan 15=350π‘₯

π‘₯ tan 15=π‘₯350π‘₯

π‘₯ tan 15=350

π‘₯tan 15tan 15

=350tan 15

π‘₯=1306π‘š

15Β° 350 m

π‘₯

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 15Β° and the plane is 350m above the control tower, what is the horizontal distance from the control tower to the airplane?

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tan 15=350π‘₯

π‘₯ tan 15=π‘₯350π‘₯

π‘₯ tan 15=350

π‘₯tan 15tan 15

=350tan 15

π‘₯=1306π‘š The plane is 1306 m away from the control tower.

15Β° 350 m

π‘₯

Page 21: Mat2793 - Angle of Elevation

Finding angle of elevation Finding a side using angle of elevation

x

Summary

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

tanπ‘₯=π‘Ÿπ‘–π‘ π‘’π‘Ÿπ‘’π‘›

π‘Ÿπ‘’π‘›=π‘Ÿπ‘–π‘ π‘’tanπ‘₯ π‘Ÿπ‘–π‘ π‘’=π‘Ÿπ‘’π‘› βˆ™ tan π‘₯

Page 22: Mat2793 - Angle of Elevation

IMAGE CREDITSBow Valley College