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.