What are the horizontal and vertical dimensions of a 23 inch diagonal if the ratio h:v is 16:9? - h i v more condition_symptoms
I'm trying to get an idea of the magnitude of this monitor.
Saturday, December 12, 2009
H I V More Condition_symptoms What Are The Horizontal And Vertical Dimensions Of A 23 Inch Diagonal If The Ratio H:v Is 16:9?
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3 comments:
First, by the theorem of Pythagoras.
a ² + b ² = c ²
16 ² + 9 ² = c ²
256 + 81 = c ²
c = √ 337
c ≈ 18.36
Thus, if the diagonal are 18,36 cm, width and height would be 16 inches and 9 inches respectively. Now its true scale of 23 inches diagonal.
You can do this using the coefficients:
23/18.36 = H/16
Solving h (both sides with 16):
h = 16 * (23/18.36)
H ≈ 20 inches
And just for the vertically:
v = 9 * (23/18.36)
v ≈ 11.3 cm
Answer:
A 23-inch diagonal (in a 16:9 widescreen) are about 20 cm wide and 11.3 cm high.
11 1 / 4 vertical, horizontal 20
Proof: 11.25 ^ 2 + 20 ^ 2 = 526.56
sq.rt 526.56 = 22.95 (Pythagoras's formula)
Here, the operation is
Let x = vertical dimension
Let Y = horizontal dimension
Then x ^ 2 + y ^ 2 = 23 ^ 2
x ^ 2 + y ^ 2 = 529
y / x = 16 / 9
16x = 9y
x = 9y / 16
Therefore 9y/16 substitute for X x ^ 2 + y ^ 2 = 529
(9y/16) ^ 2 + y ^ 2 = 529
81 and ^ 2 / 256 + y ^ 2 = 529
Multiplying all the members of 256 are
81 and ^ 2 256 ^ 2 = 529 (256)
337y ^ 2 = 135424
y ^ 2 = 135424 / 227
y ^ 2 = 401.85
Y = 20.05, which I call by 20 inches
Since y / x = 16 / 9 16x = 9y, x = 9y/16
= 9 (20) / 16
= 180/16
= 11.25 cm or 11 1 / 4
These dimensions are correct.
Salud!
Horizontal 14.72
8.28 vertical
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