Using Mathematics to Estimate a Quantity of Interest such as "How Big is the Sun?"

Students drew ray diagrams and used prior knowledge of geometry of similar triangles to calculate the diameter of the sun:

Variables Used:

• H= diameter of the sun
• h= diameter of the image of the sun
• D= distance from the sun to the pinhole
• d= distance from the pinhole to the image

Geometry of similar triangles: ratios of height to distance to pinhole are equal

• H/D=h/d
• H= (D)(h)/(d)
• (100,000,000 miles)(1 cm)/(100cm)= about 1,000,000 miles