Description
investigate the many ways that the concept of “slope” and “angle” touch our daily lives.
In this week’s lessons you will learn about some characteristics of lines and curves. Your discussion forum exercise this week is to apply the concepts of angle of inclination and slope (rise over run) to everyday ?examples.
You can go out and measure the slope something actual, like the windscreen of your car. Or you can take a picture of ?something, draw a line along its slope, and make measurements on the picture to calculate the slope. This is illustrated in the picture below.
Slope and Angle
The slope of a line and ?the angle of tilt of a line represent the same thing but they are not identical things.?
A slope of a line is a ratio; it’s the ratio of “rise over run” (rise divided by run). A slope has no units, it’s ?just a number; whereas, an angle does have units. Angles are expressed in degrees or radians. So ?what is the connection between slope and angle of tilt?
A slope of a line is the tangent of the angle of tilt of that line. (Tangent from trigonometry, like sine and cosine)?:
Slope = tan(Angle of Tilt).
You can get the angle from the slope by taking its inverse tangent.
Angle = tan-1(Slope).
Tan-1 can also ?be written as arctan, so
Angle = arctan(Slope).?
The two angles in the picture above are:
Steeper angle = arctan(0.80) = 38.7°?
Less steep angle = arctan(0.41) = 22.3°?
On to Measurement
Find an object, or a picture of an object, that is tilted.
Paste the picture of that object directly in your post.
Give the numbers for the horizontal and vertical distances you used to calculate the tilt of the object.
Give the calculated slope and angle of inclination of the object.
Tell us how you obtained the horizontal and vertical distances. Did you measure the actual object? Or did you draw lines on a picture and measure them?
Can you think of something in your daily life whose slope or angle of inclination you would like to know?
Don’t forget that you must give attribution to the source of your picture. If you took the picture yourself, say so. If you found the picture on the Internet, be sure to copy and paste the URL of the page from where you got the picture.
