Answer :
Answer:
The width and height of the old 35-inch television are 28 inches and 21 inches, respectively.
Step-by-step explanation:
35-inch television is a television whose screen has an hypotenuse ([tex]l[/tex]) of 35 inches and the aspect ratio of 4 : 3 means that 4 inches width per each 3 inches height. And by Pythagorean Theorem:
[tex]r_{l} =\sqrt{r_{w}^{2}+r_{h}^{2}}[/tex]
Where:
[tex]r_{l}[/tex] - Hypotenuse rate, dimensionless.
[tex]r_{w}[/tex] - Width rate, dimensionless.
[tex]r_{h}[/tex] - Height rate, dimensionless.
If [tex]r_{w} = 4\,in[/tex] and [tex]r_{h} = 3\,in[/tex], the hypotenuse rate is:
[tex]r_{l} = \sqrt{4^{2}+3^{2}}[/tex]
[tex]r_{l} = 5[/tex]
The width and height of the old television can be found with the help of trigonometric functions:
Width of 35-inch old television ([tex]w[/tex])
[tex]w = l\cdot \cos \theta[/tex]
[tex]w = l\times\left(\frac{r_{w}}{r_{l}} \right)[/tex]
Height of 35-inch old television ([tex]h[/tex])
[tex]h = l\cdot \sin \theta[/tex]
[tex]h = l\times\left(\frac{r_{h}}{r_{l}} \right)[/tex]
Where [tex]\theta[/tex] is the direction of the hypotenuse with respect to width, measured in sexagesimal degrees.
If [tex]r_{w} = 4[/tex], [tex]r_{h} = 3[/tex] and [tex]r_{l} = 5[/tex] and [tex]l = 35\,in[/tex], the width and height of the old 35-inch television:
[tex]w = (35\,in)\times \left(\frac{4}{5} \right)[/tex]
[tex]w = 28\,in[/tex]
[tex]h =(35\,in)\times \left(\frac{3}{5} \right)[/tex]
[tex]h = 21\,in[/tex]
The width and height of the old 35-inch television are 28 inches and 21 inches, respectively.