The similar triangle relationship by the rays of the Sun and the shadow of
the Moon indicates that their distances to Earth are proportional.
- The distance the Moon has to be from the Earth to appear the same size as the Sun is approximately 373,731.13 km.
Reasons:
The diameter of the Sun = 1,391,000 km
The diameter of the Moon = 3,475 km
The distance between the Earth and the Moon = 149,60,000 km
Required:
The distance that the Moon can be from Earth, such that the Moon appear to be the same size as the Sun.
Solution:
The vertex angle formed by the Moon and the Sun at the Earth are the
same, assuming the Moon and the Sun are in the same line, we have;
Considering the diameters of the Sun and the Moon as parallel lines, we have;
The base angles formed at the Sun and the Moon are equal
Therefore, the shadows of the Sun and the Moon form similar triangles with the Earth.
Using the relationship similar triangles, we have;
[tex]\displaystyle \frac{Disatance \ of \ the \ Sun \ from \ the \ Earth}{Diameter \ of \ the \ Sun} =\mathbf{ \frac{Distance \ of \ the \ Moon \ from \ the \ Earth}{Diameter \ of \ the \ Moon}}[/tex]
Which gives;
[tex]\displaystyle \frac{149,600,000}{1,391,000} = \mathbf{\frac{Distance \ from \ the \ Moon \ to \ the \ Earth, \ d }{3,475}}[/tex]
[tex]\displaystyle The \ distance \ from \ Moon \ to \ Earth, \ d = \displaystyle \frac{149,600,000}{1,391,000} \times 3,475 \approx 373,731.13[/tex]
The distance the Moon have to be from Earth for the Moon to appear the same as the Sun, d ≈ 373,731.13 km.
Learn more about similar triangles here:
https://brainly.com/question/16983333
