In the muon experiment, the relativistic approach yields agreement with experiment and is greatly different from the non-relativistic result. Note that the muon and ground frames do not agree on the distance and time, but they agree on the final result. One observer sees time dilation, the other sees length contraction, but neither sees both.

These calculated results are consistent with historical experiments.

The calculation will be considered from the Earth frame of reference. The length is then unaffected since it is in the Earth frame. The halflife is in the muon frame, so must be considered to be time dilated in the Earth frame. You may substitute values for the height and the muon speed in the calculation below.