Trigonometry homework

Question

Consider a 46 inch TV with aspect ratio 16:9. The aspect ratio is width-to-height, so 16:9 means 16 inches width for every 9 inches height.

Binocular vision in humans is 114∘ on average. This means if the average human can see 57∘ to the left and right of their nose in binocular vision.

Round answers to two decimal places. 

What is the width of the TV?  inches 

If your eyes are centered on the TV screen, what is the minimum distance from your eyes to the screen to still be able to see everything in binocular vision?

Answer 1

TV has a 46 inch diagonal

use the Pythagorean Theorem:

hypotenuse squared = sum of squares of the other two sides

46^2 = w^2 +h^2 where w=width, h=height w/h=16/9, w =16h/9

46^2 = (16h/9)^2 + h^2

2116 = 256h^2/81 +h^2 = 337h^2/81

171,396 = 337h^2

h^2 = 171396/337

h = sqr(171396/337) = about 22.52 inches = height

w/h = 16/9

w = 16h/9 = 16(22.52)/9 = about 40.092 inches = width