Right angle formed by moon during one of its phases with Earth and the sun, in which the distance between the moon and the sun is,
[tex]\dfrac{y}{\tan(x^o)}[/tex]
In a right angle triangle ratio of opposite side to the hypotenuse side is equal the tangent angle between adjacent side and hypotenuse side.
[tex]\tan\theta=\dfrac{b}{c}[/tex]
Here, (b) is the opposite side, (c) is the hypotenuse side and [tex]\theta[/tex] is the angle made between them.
The distance between the Earth and Moon is y units and the angle between the distance of the Earth from Sun and the distance of the Moon from Sun is x degrees.
The image of the right angle which moon forms with the Earth and the sun during one of its phases is attached below.
Let the distance from the Moon to the Sun is p units.
As this length is the hypotenuse side of the right angle triangle and The distance between the Earth and Moon is opposite side of right angle triangle.
Thus by the property of right angle triangle,
[tex]\tan(x^o)=\dfrac{y}{p}\\p=\dfrac{y}{\tan(x)}[/tex]
Hence, the distance between the moon and the sun is,
[tex]\dfrac{y}{\tan(x^o)}[/tex]
Learn more about the right angle triangle property here;
https://brainly.com/question/22790996
