Use parallax to measure the size of a room

Your job is to measure the distance from one side of a room to the other -- without actually crossing the room.

The basic idea behind "parallax" is explained on this webpage (and in many other places, too). If you measure the distance along one wall of a room, and then determine very carefully the angle from each corner of the room to a point on the middle of the far wall, you can use basic geometry to calculate the distance to that far wall.

Choose a good room for this experiment; if necessary, place a prominent object P on the middle of the far wall. Acquire the equipment you'll need: something with which to measure distance (tape measure, yardstick, etc.), and something with which to measure an angle (a protractor, or a yardstick and a calculator).
Take a photo or two of the room, and make a diagram showing its main features.
Measure the baseline distance b along the near wall of the room. Write it down.
Measure the angle α from each corner of the room to the middle of the far wall. Write it down.
Compute the size of the parallax angle θ. Write it down.
Use your measurements, and some geometry, to compute the distance D across the room. Show all your work.
Now, measure the distance D directly.
How close was your calculated distance to the real distance?

One example of a real parallax experiment involves pictures taken from Earth and from the New Horizons spacecraft, in the far reaches of the Solar System. You can read about that experiment at

Compare the size of your angle θ to the size of the parallax angle I measured in the New Horizons experiment.

Scan or photograph all your drawings and notes, creating a single PDF file with all the material. Submit the PDF file via the myCourses "Assignments" facility.