Given the measurement of the hypotenuse of a right-angle triangle, and the ratio of the other two sides, how would figure out their lengths? Basically, how do you figure out the height and width of a monitor or TV if all you know is the size and the aspect ratio? Can't seem to find a way to by Googling it.

You mean the ration of a side to the hypotenuse?

given H and (aspect ratio)

H = sqrt( a^2 + B^2)

a/b = (aspect ratio)

solve simultaniously

if you give me the values I can do it, but I can't explain it any better sorry.

Basically, tell me the height and width of a 50" TV with a 16:9 aspect ratio.

Kay.

1) Find out the horizontal distance x of the monitor.
2) Find out the aspect ratio in w:h.
3) Construct as a rt. angled triangle with x as the hypotenuse and a and b as the other two sides.

You should have x[sup]2[/sup] = a[sup]2[/sup] + b[sup]2[/sup]

4) Let a = wy and b = hy.
5) Substitute in and solve for y.
6) Find out a and b.

As your solution, it comes to 43.5" by 24.5". I think. Assuming my brain's functioning properly.

[QUOTE=Numenor King]given H and (aspect ratio)

H = sqrt( a^2 + B^2)

a/b = (aspect ratio)

solve simultaniously

if you give me the values I can do it, but I can't explain it any better sorry.[/QUOTE]

Yeah, you could then say (ar = aspect ratio):

H = sqrt( (ar *b)^2 + b^2) by substituting ar * b for a
H^2 = b^2 * ( ar^2 + 1)

Then you can finally derive the answer for one of the sides:

H^2 / ( ar^2 + 1) = b^2 -> sqrt( H^2 / ( ar^2 + 1) ) = b


Now that you have b, you can easily find a:

a = b * ar

Hope that helps

disregard my last post.

trig is easier and it accualy works.

right triangle:
H = 50
a = ?
b = ?

Similer triangle:
H = ?
a = 16
b = 9

t is the angle between the long side and 50

tan(p) = 9/16
p = arctan(9/16)

p = about 29.36 degrees

sin(p) = b/50

b = 50sin(p) = about 24.5in

a = 50cos(p) = about 43.5in

there thats better

so the TV is: 43.5 X 24.5 in

(16x)[sup]2[/sup] + (9x)[sup]2[/sup] = 50[sup]2[/sup]

256x[sup]2[/sup]+ 81x[sup]2[/sup] = 2500

337x[sup]2[/sup] = 2500

x[sup]2[/sup] = 7.418

x = 2.7236

therefore
16x ~= 43.6 in = width
9x ~= 24.5 in = height
which confirms answers by other methods (though I rounded so it's a decimal off)

Btw, I think this is the easiest way :p they gave you a ratio, so just use the ratio
Don't have to bother with all this trig

Pommy's method was what I was looking for. I was trying to solve it that way as well but just could never work it out correctly. It really has been a while since high school.