What is the height of the screen?

Question

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 5.7 feet and the horizontal distance from you to the screen is 11 ft. The bottom of the screen is 6 feet from the ground. Approximate the height of the screen to the nearest tenth.

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Answer 1 · 2018-03-29T22:18:58

#h=20.9# feet

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The triangles in the picture are shown below:

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Triangles #Delta ADB# and #DeltaADC# are similar right triangles by virtue of the Angle Angle theorem. because:

In triangle #DeltaABD#, #/_ABD + /_BAD = 90^@#

In triangle #DeltaABC#, #/_ABD + /_ACB = 90^@#

Therefore,

#/_BAD = /_ACB#

And because the two triangles also have a #90^@# angle each, they are similar.

This means that the ratios of their corresponding sides are the same:

#5.7/11=11/(DC)#

#DC=121/5.7=21.2# feet

#BC=BD+DC=5.7+21.2=26.9# feet

Since the bottom of the screen is #6# feet above the ground, the height of the screen is:

#h=26.9-6=20.9# feet