Math 11AW Unit 4: Slopes and Rates



Math 11AW Unit 4: Slopes and Rates. Name: _________________ Date: _____________ Block: ______

Lesson Notes 4.4: Angle of Elevation and Slope.

Try these.

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Leo is installing a guy wire on a telephone pole.

• The wire needs to be anchored 50 ft from the base of the pole.

• The wire must be attached to the pole at a height of 30ft.

What is the angle of elevation of the guy wire with the ground?

Example 1) Bev makes handcrafted kites. She is testing a new kite. She looks up along the kite string at an angle of elevation of 20°. What is the slope of Bev's line of sight to the kite? How is the slope related to the angle of elevation?

Example 2) Calculate the missing angles and the slope of the hypotenuse.

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Example 3) Albert works as a ski instructor. He has read that human-triggered avalanches occur

most often on slopes with angles of elevation between 35° and 45°.

a) What are the slopes of these two angles of elevation?

b) What are the percent grades?

Example 4) Aurena is installing a pipe for drainage. The system requires a drop of 1.5 cm for every 2.5 m of horizontal distance.

a) What is the slope of the pipe?

b) How much drop will she need if the horizontal distance is 12 m?

Math 11AW Unit 4: Slopes and Rates. Name: _________________ Date: _____________ Block: ______

Assignment 4.4: Angle of Elevation and Slope.

1) Calculate the missing angles and the slope of the hypotenuse.

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2) A surveyor is sighting to the top of a building. The horizontal distance to the building is 67 m. The sight line forms an angle of elevation of 32°.

a) How high above the surveyor's instrument is the top of the building?

b) The surveyor is sighting from a height of 1.4 m. How tall is the building?

3) Johanna and Noel are roofers. Do they agree?

• Johanna measures roof pitch in degrees. She says the angle of elevation of a new roof should be 26.5°.

• Noel measures roof pitch as a grade. He says the grade of the roof should be 50%.

4) Claire is putting up patio lights. She rests a ladder against the house. For safety, the distance from the foot of the ladder to the house should be about one quarter of the ladder's height.

a) What should the slope of the ladder be?

b) How far away should the foot of the ladder be from the house?

c) What angle of elevation does the ladder make with the ground, to the nearest degree?

5) a) The Bow in Calgary was the tallest building in Western Canada when it was completed. How

much taller is The Bow than the other building in this diagram?

b) Does the side opposite the 63° angle match the rise or the run of the triangle in Part a)?

6) The roof of one house has a pitch of 4.2 : 12. The roof of a second house has a pitch of 7.8 : 20. Which roof is steeper?

7) One of the steepest railways in the world is the Lisbon tram in Portugal. In one section, it has a grade of 13.5%.

a) Express this as a slope.

b) Calculate the angle of elevation.

c) What is the rise for a run of 15 m?

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