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answers:
spot a say: They get astronomers to measure it using geometry and the position of Venus.
Radar does bounce off the sun. NASA does some radar echoes
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Morningfox say: Some good answers by other people. I will add one small note: we don't actually measure the distance to the sun. What is measured is the distance to the focal point of the orbits of the planets. We then assume that the center of the sun is at that focal point. (Adjustments are made because Jupiter, for example, doesn't orbit the sun ... it orbits the system of Sun + Mercury + Venus + Earth + Mars.)
Some special measurements, rarely done, have shown that this is off by a few hundred meters, probably because the sun's mass is not *exactly* symmetrical. The measurements are difficult because it's so hard to find the precise location of the surface of the sun.
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tham153 say: astronomers measured that over a century before NASA as created
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Brigalow Bloke say: Following a suggestion from Edmund Halley for whom the comet is named, expeditions were sent out by various nations to observe the transits of Venus in 1761 and 1769.
In 1769 James Cook RN arrived at Tahiti to time the transit of Venus across the face of the Sun along with a ship load of botanists and other scientists. The day turned out to be cloudless but the measurements were spoiled by something they had not bargained for, the time that the planet began and ended the transit was uncertain due to optical effects. In other parts of the world similar measurements were made. Just the same, the result that Cook's party obtained was within 1% of the modern value.
The intent was to determine the distance to the Sun. This would improve navigation and land surveying.
Later, Cook sailed south and east, then west and first mapped the entire coast of New Zealand and from there moved west in search of the east coast of the southern continent which was known to exist, from Dutch and Portuguese landfalls on the west and north coasts. He found it and mapped the entire east coast of what is now Australia. He named it New South Wales for some unknown reason.