Answer :
In order to determine the height of the screen of the drive-in movie theater, we must have to create the figure as per the question statement.
The height of the screen of the drive-in movie theater is [tex]35\:\rm ft[/tex].
Given:
The vertical distance from the ground to your eye is 5.5 ft.
The distance from you to the screen is 14 ft.
The bottom of the screen is 6 feet from the ground.
Refer the attached figure, [tex]\Delta ADB[/tex] and [tex]\Delta ADC[/tex] are the similar triangles.
Thus, the triangle [tex]\Delta ABD[/tex] is,
[tex]\angle ABD+\angle BAD=90^{\circ}[/tex]
Consider the triangle [tex]\Delta ABC[/tex].
[tex]\angle ABD+\angle ACB=90^{\circ}[/tex]
From the above equation [tex]\angle BAD=\angle ACB[/tex]
The ratios of their corresponding sides are the same,
[tex]\dfrac{5.5}{14}=\dfrac{14}{DC}\\DC=\dracf{196}{5.5}\\DC=35.63 \:\rm feet[/tex]
Calculate the length BC.
[tex]BC = 5.5 + 35.63 \\BC= 41.13\:\rm ft[/tex]
The bottom of the screen is 6 feet from the ground.
[tex]h = 41.13 - 6\\h = 35.13\: \rm ft[/tex]
Thus, the height of the screen of the drive-in movie theater is [tex]35\:\rm ft[/tex].
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