Fun Photography and Similar Triangles

In a recent department meeting, one of my colleagues reminded us of the fun you can have with similar triangles and perspective photography. As an example, this photo was taken at  the Salt Flats in Uyuni, Bolivia.

By knowing some of the dimensions in the picture, we could figure out how far away I had to stand from the camera.

Note that you cannot meaure the length of me on the photo because a larger or smaller photo would mean that I was closer or further away from the camera which is not possible. The distance has to be the actual distance from the floor to my fiance’s hand.

We have two similar triangles here and so there is a scale factor which links the corresponding lengths of the triangle. In this case the scale factor, k =3.6 (k=1.8/0.5).

Hence the length of the base of the bigger triangle is 1.5 m x 3.6 = 5.4 m. Unfortunately I don’t have the actual distance I was from the camera when this picture was taken but I do remember being about 5 metres away.

Next time you’re teaching ratio/similar triangles you should grab the cameras and get the students to do some perspective photography.

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