If a TV screen with an aspect ration of 16:9 measures 48cm diagonally, what are the height and width measurments of the screen?
The aspect ratio width to diagonal is
16: (sqrt(16^2+ 9^2))
16:18
so..
16/18= w/48
and for height
9/18=h/48
To find the width and height measurements of the TV screen with a diagonal measurement of 48cm and an aspect ratio of 16:9, you can use the following steps:
1. Calculate the ratio of the width to the diagonal:
Width Ratio = 16 / √(16^2 + 9^2) = 16 / √(256 + 81) = 16 / √337 ≈ 16 / 18.357 = 0.872
2. Multiply the width ratio by the diagonal measurement to find the width:
Width = Width Ratio * Diagonal = 0.872 * 48cm = 41.856cm ≈ 41.9cm
3. Calculate the ratio of the height to the diagonal:
Height Ratio = 9 / √(16^2 + 9^2) = 9 / √(256 + 81) = 9 / √337 ≈ 9 / 18.357 = 0.490
4. Multiply the height ratio by the diagonal measurement to find the height:
Height = Height Ratio * Diagonal = 0.490 * 48cm = 23.52cm ≈ 23.5cm
Therefore, the width of the TV screen is approximately 41.9cm and the height is approximately 23.5cm.