How do you approximate the height of the screen to the nearest tenth?

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 feet and the horizontal distance from you to the screen is 13 feet. The bottom of the screen is 6 feet from the ground.enter image source here

1 Answer
May 29, 2018

32.8 feet


Since the bottom triangle is right-angled, Pythagoras applies and we can calculate the hypotenuse to be 12 (by #sqrt(13^2-5^2)# or by the 5,12,13 triplet).

Now, let #theta# be the smallest angle of the bottom mini triangle, such that

#tan(theta) = 5/13# and thus #theta = 21.03^o#

Since the big triangle is also right-angled, we can thus determine that the angle between the 13 foot side and the line connecting to the top of the screen is #90-21.03=68.96^o#.

Finally, setting #x# to be the length from the top of the screen to the 13 foot line, some trigonometry gives

#tan(68.96)=x/13# and therefore #x=33.8# feet.

Since the screen is 1 foot above the ground, and our calculated length is from the person's eye height to the top of the screen, we must subtract 1 foot from our #x# to give the height of the screen, which is #32.8# feet.