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