Angle of Elevation and Slope
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
tanπ₯=πππ πππ’π
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
tanπ₯=πππ πππ’π
tanπ₯=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
tanπ₯=πππ πππ’π
tanπ₯=514
tanβ1 tan π₯=tanβ 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
tanπ₯=πππ πππ’π
tanπ₯=514
tanβ1 tan π₯=tanβ 1514
π₯=tanβ1514
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
tanπ₯=πππ πππ’π
tanπ₯=514
tanβ1 tan π₯=tanβ 1514
π₯=tanβ1514
π₯=19.65 Β°
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
tanπ₯=πππ πππ’π
tanπ₯=514
tanβ1 tan π₯=tanβ 1514
π₯=tanβ1514
π₯=19.65 Β°
x
5 ft
The angle of elevation of Staceyβs roof is 19.65Β°.
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₯
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₯=πππ πππ’π
15Β° 350 m
π₯
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₯=πππ πππ’π
tan 15=350π₯
15Β° 350 m
π₯
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₯=πππ πππ’π
tan 15=350π₯
π₯ tan 15=π₯350π₯
15Β° 350 m
π₯
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₯=πππ πππ’π
tan 15=350π₯
π₯ tan 15=π₯350π₯
15Β° 350 m
π₯
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₯=πππ πππ’π
tan 15=350π₯
π₯ tan 15=π₯350π₯
π₯ tan 15=350
15Β° 350 m
π₯
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₯=πππ πππ’π
tan 15=350π₯
π₯ tan 15=π₯350π₯
π₯ tan 15=350
π₯tan 15tan 15
=350tan 15
15Β° 350 m
π₯
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₯=πππ πππ’π
tan 15=350π₯
π₯ tan 15=π₯350π₯
π₯ tan 15=350
π₯tan 15tan 15
=350tan 15
15Β° 350 m
π₯
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₯=πππ πππ’π
tan 15=350π₯
π₯ tan 15=π₯350π₯
π₯ tan 15=350
π₯tan 15tan 15
=350tan 15
π₯=1306π
15Β° 350 m
π₯
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₯=πππ πππ’π
tan 15=350π₯
π₯ tan 15=π₯350π₯
π₯ tan 15=350
π₯tan 15tan 15
=350tan 15
π₯=1306π The plane is 1306 m away from the control tower.
15Β° 350 m
π₯
Finding angle of elevation Finding a side using angle of elevation
x
Summary
tanπ₯=πππ πππ’π
tanπ₯=πππ πππ’π
ππ’π=πππ πtanπ₯ πππ π=ππ’π β tan π₯
IMAGE CREDITSBow Valley College