People who design products for consumers use their knowledge of quadrilaterals and other shapes on a daily basis. Suppose an engineer receives the following note from the head of marketing, who has just returned from a big consumer electronics convention.
Buyers want a 100 inch TV! We need to get the design specs to our manufacturing plant in Beijing by tomorrow so that we can roll out our new 100 inch line. Otherwise, our competitors are going to turn one out before we do, and then they'll have a head start on the holiday shopping season. You need to make the aspect ratio 16:9, that's what people want nowadays.
It's a brief note, lacking in some key details. However, if the engineer knows her geometry well, she can figure out the specs for the mega-set fairly quickly. Watch this video to see how.
As you watch this video, use the study guide to follow along if you'd like. Click the button below to download the study guide.
When a local electronics store advertises their 46 inch flat panel TVs, they don't expect the general public to know that these TVs aren't 46 inches wide, they're not even 46 inches tall. Instead, the dimension is measured along the diagonal of the rectangular screen. In this video, I'll show you how to determine the width and height of a TV if you know it's diagonal measurement.
TVs are constructed follow a specific aspect ratio, or ratio of width to height. That ratio for modern TV screens is usually 16:9, for every 16 inches of width, the TV will have 9 inches of height. This is nice for us, since a TV screen of any size will be similar in shape to a rectangle that is 16 inches wide and 9 inches tall… Since these shapes are similar, then the side lengths are proportional.
Label your rectangles with known information – the diagonal of the TV screen and the width and the height of the similar rectangle… Now, use the Pythagorean Equation to determine the length of the diagonal in that similar rectangle… The length of the diagonal is approximately 18.36 inches . Now we can use proportions to identify the width and height of the TV screen … The length of diagonal divided by height of the rectangle is equal to the length of the diagonal divided by the height of the TV screen. The same goes for the height.
We can use cross products to determine the value for w and h that represent the width and height of the TV screen … This work shows us that the width of the TV screen is approximately 40.09 inches, and the height is approximately 22.55 inches.
This technique can be used for a TV screen or monitor of any size or aspect ratio. So if a screen has an aspect ratio of 21:9 or 4:3, you can determine the height and width of the screen by using a few simple steps. Try a problem like this on your own to determine if your new 100 inch TV will fit on a wall that's only 8 feet wide and 8 feet tall. Good luck!
Question
What does it mean for a TV to have an aspect ratio of of 16:9?
