A student holds a disc of diameter 100 mm. It just blocks the sun when heldat a distance of1m from the eye. If the distance from sun to the disc is 1.5 x108km, determine the diameter of the sun.
Question
A student holds a disc of diameter 100 mm. It just blocks the sun when heldat a distance of1m from the eye. If the distance from sun to the disc is 1.5 x108km, determine the diameter of the sun.
Solution
To determine the diameter of the sun, we can use the concept of similar triangles.
Let's denote the diameter of the sun as D. We know that the distance from the sun to the disc is 1.5 x 10^8 km, which is equivalent to 1.5 x 10^11 mm (since 1 km = 10^6 mm).
We also know that when the disc is held at a distance of 1 m from the eye, it just blocks the sun. This means that the diameter of the disc, which is 100 mm, is equal to the diameter of the sun's image formed on the retina of the eye.
Using the concept of similar triangles, we can set up the following proportion:
D/1.5 x 10^11 = 100/1
Cross-multiplying, we get:
D = (100 * 1.5 x 10^11) / 1
Simplifying, we find:
D = 1.5 x 10^13 mm
Therefore, the diameter of the sun is approximately 1.5 x 10^13 mm.
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