Containment by Christian Cantrell. It was published in 2010, which fits neatly with the time you remember reading it.
The scene you remember is when the protagonist Arik is using the shadows of the antennae to measure the circumference of the planet he is on. The people have been told they are on Venus, but when Arik does the measurements he finds:
The antennas and the difference between the lengths of the shadows that they cast formed a theoretical triangle which Arik needed to finish solving before he could go any further. He used a visual triangle calculator to figure out the values he didn't have yet. The most important value was the angle between the antenna and the 1.57 millimeter shadow which turned out to be .009 degrees. Arik needed to figure out what fraction of the planet's circumference the distance between the two antennas represented which he knew could be expressed as 360 over .009, or 40,000 kilometers.
The answer was wrong. The difference between his results and the actual circumference of Venus was 5% — a margin of error worse than that achieved by Eratosthenes who used nothing more than a deep well, a stick, and a man he hired to pace out the 800 kilometers between the two landmarks. Arik began the experiment over again, starting with two new screenshots of the video feeds, and allowed the computer to calculate down to as many decimal places as it needed. Once again, Arik found that even though he was 250 million kilometers away, he had somehow calculated, with great precision, the circumference of the Earth.
