Adapted from Geometry Labs, by Henri Picciotto
Using Slope Angles
- How tall is the flagpole?
- How far is the boat from the base of the cliff?
For the remaining problems, make your own sketches.
- Looking down at a boat from a 30 meter high lighthouse, an observer measures an angle of 15° below the horizontal. How far is the boat from the base of the lighthouse?
- A ski-lift rises 200 meters for a run of 250 meters. What angle does it make with the horizontal?
- At a certain time of day, a 33 ft flagpole casts a 55 ft shadow. What is the angle made by the sun's rays with the horizontal?
- The banister of a straight staircase makes an angle of 39° with the horizontal. The stairs connect two floors that are 10 feet apart.
- How much horizontal space does the staircase take?
- If steps are 8 inches high, how wide are they?
- You stand on a cliff, looking down at a town in the distance. Using a map, you find that the town is 1.2 kilometers away. The angle your line of vision makes with the horizontal is 11.3°. How high is the cliff?
- A right triangle has a 15° angle and a short leg of 18 units. How long is the long leg?
- A right triangle has a 75° angle and a short leg of 18 units. How long is the long leg?
- The problems in this activity have been rigged to only use angles and slopes that you included in the tables. Explain how to use the 10-cm circle to solve problems of this type involving any angle at all.
- Find the angles for slopes of 10, 25, 100. What happens as the slope gets bigger and bigger?