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A Scale for the Solar System

Stage: 4 Challenge Level: Challenge Level:1

Lukaz Smith, from Parkside School, sent in the following correct approach to finding the ratio of the Earth-Sun and Venus-Sun distances (diagram added to help clarify the solution)

If you said the Earth to sun distance was 1 astronomical unit ($a$ in diagram), then you could simply measure the angle ($\theta$ in diagram) between Sun, Earth and Venus, when you knew that there was a 90 degree angle between Earth, Sun and Venus. Then you just find the tangent of the angle, so it's 1 : $\tan \theta$ as the ratio of Earth to Sun distance and Venus to Sun distance.
Diagram showing Sun, Venus and Earth on corners of right angle triangle