The size of a computer monitor is given by the length of the diagonal of the screen.The ratio of the height to the width of wide screen monitors is 9:16. Find the expressions for the width and height of a wide screen monitor in terms of the lengthy of its diagonal.

tan 29.3° = 9/16, so

width = diagonal * sin 29.3°
length = diagonal * cos 29.3°

thank you

Let's assume that the length of the diagonal of the wide screen monitor is represented by D.

We know that the ratio of the height to the width of the wide screen monitors is 9:16. Therefore, we can express the height as 9x and the width as 16x, where x is a scaling factor.

To find the expressions for the width and height of the wide screen monitor in terms of its diagonal length, we can use the Pythagorean theorem.

According to the Pythagorean theorem:
(Diameter)^2 = (Height)^2 + (Width)^2

Substituting the values we have:
D^2 = (9x)^2 + (16x)^2
D^2 = 81x^2 + 256x^2
D^2 = 337x^2

Taking the square root of both sides, we get:
D = √(337x^2)

To express the width and height in terms of the diagonal length, we divide both sides of the equation by x:
D/x = √337

Therefore, the expressions for the width and height of the wide screen monitor in terms of its diagonal length (D) are:
Width = 16(D/x)
Height = 9(D/x)

To find the expressions for the width and height of a widescreen monitor in terms of the length of its diagonal, we need to use the given ratio of the height to the width.

Let's assume that the width of the widescreen monitor is represented by "w" and the height is represented by "h". We are given that the ratio of the height to the width is 9:16, which means:

h/w = 9/16

We can cross-multiply this ratio to find an expression for the height in terms of the width:

16h = 9w

Similarly, to find an expression for the width in terms of the height, we can cross-multiply the ratio:

9w = 16h

Now, let's consider the length of the diagonal of the monitor, which is given. The Pythagorean theorem allows us to relate the height, width, and diagonal length:

(diagonal)^2 = (height)^2 + (width)^2

Let's substitute our expressions for the height and width into this equation:

(diagonal)^2 = (16h)^2 + (9w)^2

We can simplify this equation further by substituting 16h for 9w (using the expression we found earlier):

(diagonal)^2 = (16h)^2 + (9w)^2
(diagonal)^2 = (16h)^2 + (9(16h))^2
(diagonal)^2 = 256h^2 + 729h^2
(diagonal)^2 = 985h^2

Finally, to get the expressions for the width and height in terms of the diagonal length, we can solve for "h" in the equation above:

h = sqrt((diagonal)^2 / 985)

Now, we can substitute this expression for "h" in any of the previous equations to find the expression for the width "w", such as using h/w = 9/16:

w = (16h) / 9
w = (16 * sqrt((diagonal)^2 / 985)) / 9

Therefore, the expressions for the width and height of a widescreen monitor in terms of the length of its diagonal are:

Width: w = (16 * sqrt((diagonal)^2 / 985)) / 9
Height: h = sqrt((diagonal)^2 / 985)