You want to determine the height of the screen at a drive-in movie theater. You use a cardboard square to line up the top and bottom of the screen structure. The vertical distance from the ground to your eye is 5.5 ft and the horizontal distance from you to the screen is 14 ft. The bottom of the screen is 6 feet from the ground. Approximate the height of the screen to the nearest tenth.

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 .

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, and are the similar triangles.

Thus, the triangle is,

Consider the triangle .

From the above equation

The ratios of their corresponding sides are the same,

Calculate the length BC.

The bottom of the screen is 6 feet from the ground.

Thus, the height of the screen of the drive-in movie theater is .

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35ft

Step-by-step explanation:

Triangle ADB and ADC are similar triangles

Triangle ABD: Angle ABD + Angle BAD = 90°

Triangle ABC: Angle ABD + Angle ACB = 90°

Angle BAD = Angle ACB

5.5/14 = 14/DC

5.5DC = 196

DC = 196/5.5

DC = 35.63ft

BC = BD + DC

BD = 5.5

BC = 5.5ft + 35.63ft = 41.13ft

Bottom of screen is 6ft above the ground ;

Therefore,

h = 41.13ft - 6ft

h = 35.13ft

h = 35ft to the nearest tenth