He moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below:

A right angle triangle is shown with the Earth at the right angle. The acute angle between the line joining the Earth and the Sun and the Sun and the moon is x degrees. The distance between the Earth and the Sun is y.

A scientist measures the angle x and the distance y between the Earth and the Sun. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the moon and the Sun.

Question

Mathematics

Giancarlo

7 August, 18:07

He moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below:

A right angle triangle is shown with the Earth at the right angle. The acute angle between the line joining the Earth and the Sun and the Sun and the moon is x degrees. The distance between the Earth and the Sun is y.

A scientist measures the angle x and the distance y between the Earth and the Sun. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the moon and the Sun.

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Answers (1)

Know the Answer?

Eliana Ray · Answer 1

Okay I made my own graphic. : - )

Let's call the Earth to Moon distance as "z"

If the astronomer can determine angle "x" and if he calculates the distance "y"

then

tangent (x) = z / y

distance z = y * tangent (x)