Video & Camera Equipment

camera platform



A photographer points a camera at a painting on a nearby wall, forming an angle of 48º with the camera platfor?

A photographer points a camera at a painting on a nearby wall, forming an angle of 48º with the camera platform. If the camera is 56 feet from the wall, how high above the platform is the painting, to the nearest hundredth of a foot?

how do i do this, or whats the answer?

This is a trigonometry question. Let’s draw a diagram.

…| <--- wall
...|
...|| <--- painting
_.||
^..||.
|..||...
h.|......
|..|........
v_|┐_48°_____ <--- camera platform
...|............|
...|<- 56' ->|

So, we’ve got a 48 degree angle between the camera platform and the center of the picture, and the camera is 56 feet from the wall. We’re looking for h, the height of the picture above the platform.

We have to make a few assumptions here. First, we assume that the camera platform makes a 90 degree angle with the wall. Second, we assume that the camera is centered on the center of the painting, and the height will be measured to the center of the painting. Both of those seem pretty reasonable.

We also assume that the painting has zero thickness – that it doesn’t stick out from the wall at all, and thus doesn’t cut into the 56 foot measurement. Another assumption is that the camera height is 0 – that the lens is exactly at the height of the platform. Both of those assumptions are okay as simplifications, but they’re not the same as reality. But we’ll go ahead and make them, and discuss how they affect the answer later.

So, we have a trigonometry relationship that says for a right triangle,

tan Θ = opposite/adjacent

In this case, Θ = 48°, the opposite side is h, and the adjacent side is 56 feet. So,

tan 48° = h / 56 ft
h = 56 ft * tan 48°

You can plug that into a calculator (make sure you’re working in degrees and not radians!) to find

h = 62.1943… ft

Rounded to the nearest hundredth,

h = 62.19 ft

Now, I have a problem with this – why would you need to be so precise, down to the hundredth of a foot, when you have to make assumptions that affect the answer much more than a hundredth of a foot?

Let’s look at the thickness of the painting. Say it sticks out from the wall 2 inches. Then we would modify our equation, to

tan 48° = h / [56 ft - (2 in * 1 ft/12 in)]
h = [56 ft - (2 in * 1 ft/12 in)] * tan 48°
h = 62.0091… ft
h = 62.00 ft

See? Even that 2 inch thickness affects the answer by more than a hundredth of an inch!

Now, what about the height of the Camera Lens above the platform? Let’s say your average camera is 3 inches high, and the center of the lens is half of that, 1.5 inches from the bottom. Then you have this situation:

…| <--- wall
...|
...|| <--- painting
_.||
^..||.
|..||...
h.|......
|..|........
|..|┐_48°_____ <--- camera lens
v_|___________ <--- camera platform
...|............|
...|<- 56' ->|

where the distance between the camera platform and the lens is 1.5 inches (and that’s before we account for rotation of the camera!). Then your equation becomes

tan 48° = [h - (1.5 in * 1 ft/12 in)] / 56 ft
h = 56 ft * tan 48° + (1.5 in * 1 ft/12 in)
h = 63.6943… ft

So that makes an even bigger difference! So, ask your teacher what’s the point of measuring the height to the nearest hundredth, if the assumptions you make affect the answer by an inch and a half!

I hope that helps you out! (Forgive my rant, but maybe that discussion might get you some extra credit.)

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