Siddharth and Ryan used indirect measurement and similar triangles to calculate the height of a soccer net. They measured their own heights and shadow lengths, as well as the shadow length of the net. By setting up proportions between the triangles formed, they were able to calculate the height of the net, which they determined to be approximately 270.9 cm. Their measurement may not be exact due to changes in shadow lengths throughout the day as the sun's position changes.