No, there's not enough information to calculate the depth.
The _size_ of the (image of the) shadow is about the same as the size of the (image of the) object casting it, so that tells us nothing. (This ignores perspectivic effects, which depends on camera position and other parameters that we have no chance of estimating here anyway).
We'd have better hope of deriving something from the _position_ of the shadow relative to the floating sunbather on the image, but there's still no luck there, because we don't have any good information about the exact position of the sun then the photo was taken -- nor about which angle the image was taken from. Either of these lacks would make it imposible to conclude anything.