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

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

Ella Armstrong · Accepted Answer

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.

Parker Allen · Answer

undefined To approximate the height of the screen to the nearest tenth, you would measure the height of the screen using a ruler or measuring tape, ensuring that the measurement is accurate. Then, you would round the measurement to the nearest tenth using the appropriate rounding rules. For example, if the measured height is 18.64 inches, you would round it to 18.6 inches. If the measured height is 22.78 inches, you would round it to 22.8 inches.