Your mother always told you not to sit too close to the TV. But sitting too far away from a small television is annoying because the picture looks too small. On the other hand, sitting very close to a large television is also not ideal because you can't focus on the whole thing at once.

Given a television of a certain size, where's the best place to put the couch? This lesson uses right triangle trigonometry and a rational function to explore the percent of your visual field that is occupied by the area of a television.

Students will

Use right triangle trigonometry to find the visible width, height, and viewing area for various distances

Find and plot the percent of your field of view filled by a 60-in. TV for various distances

Write a rational function for the percent of your visual filled by a 60-in. TV in terms of distance from the TV

Solve, algebraically or by graphing, the function to find the distance where the TV fills 100% of your view

Before you begin

Students should be able to apply trigonometric ratios to find an unknown side length of a right triangle. They should be able to calculate the area of a rectangle, and calculate a percent area given a part and a whole. They will be asked to generalize a repeated percent-area calculation and write a rational function. This lesson could be a great way to contextualize a function that is neither linear nor exponential. Finally, students will be asked to solve their equation, through either algebraic manipulation or graphically with technology.

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Mathalicious lessons provide teachers with an opportunity to teach standards-based math through real-world topics that students care about.

How have video game console speeds changed over time? Students write an exponential function based on the Atari 2600 and Moore's Law, and see whether the model was correct for subsequent video game consoles.

Topic:
Building Functions (BF), Interpreting Categorical and Quantitative Data (ID), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)