SOLUTION: 1. triangle with leg 14 and X and hypotenuse x+2. how do you solve that? AND 2. The aspect ratio of a TV screen is the ratio of the width to

Algebra ->  Pythagorean-theorem -> SOLUTION: 1. triangle with leg 14 and X and hypotenuse x+2. how do you solve that? AND 2. The aspect ratio of a TV screen is the ratio of the width to       Log On


   



Question 954559: 1.
triangle with leg 14 and X and hypotenuse x+2. how do you solve that?
AND
2.
The aspect ratio of a TV screen is the ratio of the width to the height of the image. S regular TV has an aspect ratio of 4:3. Find the height and width of a 42-inch TV screen to the nearest tenth of an inch. (The measure given is the length of the diagonal across the screen.)
AND
3.
A "wide-screen" TV has an aspect ratio of 16:9. Find the length of a diagonal on a wide-screen TV screen that has the same height as my second question.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1.
triangle with leg a=14 and b=x and hypotenuse c=x%2B2
if given hypotenuse means you have right-angle triangle, so you use Pythagorean theorem:
c%5E2=a%5E2%2Bb%5E2
%28x%2B2%29%5E2=14%5E2%2Bx%5E2
cross%28x%5E2%29%2B4x%2B4=196%2Bcross%28x%5E2%29

4x=196-4
4x=192
x=192%2F4
x=48-> other leg
and hypotenuse x%2B2=50
so, your triangle has sides length: a=14, b=48, and c=50

2.
given: aspect ratio of 4%3A3
Find the height and width of a 42-inch TV screen to the nearest tenth of an inch. (The measure given is the length of the diagonal across the screen.)
let length be L, width W
given: L%3AW=4%3A3
so, 3L=4W => L=4W%2F3
also given that is 42-inch TV screen, means its diagonal is d=42in
you know that diagonal splits TV screen into two right-angle triangles whose legs are length L and width W
use Pythagorean theorem again:
d%5E2=L%5E2%2BW%5E2....since L=4W%2F3, we can substitute it
d%5E2=%284W%2F3%29%5E2%2BW%5E2 ...plug in value for d
%2842in%29%5E2=%284W%2F3%29%5E2%2BW%5E2
1764in%5E2=16W%5E2%2F9%2BW%5E2
1764in%5E2%2A9=%289%2A16W%5E2%29%2F9%2B9W%5E2
15876in%5E2=16W%5E2%2B9W%5E2
15876in%5E2=25W%5E2
W%5E2=15876in%5E2%2F25
W%5E2=635.04in%5E2
W=sqrt%28635.04in%5E2%29
highlight%28W=25.2in%29
now find the length:

L=4W%2F3
L=%284%2A25.2in%29%2F3
highlight%28L=33.6in%29

3.
A "wide-screen" TV has an aspect ratio of 16:9. Find the length of a diagonal on a wide-screen TV screen that has the same height as my second question.
let height be W from second question:highlight%28W=25.2in%29
given: L%3AW=16%3A9
so, 9L=16W => L=16W%2F9=>L=%2816%2A25.2in%29%2F9=>highlight%28L=44.8in%29
d%5E2=L%5E2%2BW%5E2....since L=44.8in and W=25.2in
d%5E2=%2844.8in%29%5E2%2B%2825.2in%29%5E2
d%5E2=2007.04in%5E2%2B635.04in%5E2
d%5E2=2642.08in%5E2

d=sqrt%282642.08in%5E2%29
d=51.40116730192029in
highlight%28d=51.4in%29