The 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 moon is y.

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

There is nothing "as shown below". But if I'm careful, I think I can

still handle this one.

I'd like to start off by asking you how the scientist might go about

measuring the angle 'x'? Just because I'm curious.

Be that as it may, and I'll assume that it is, the three bodies form a right triangle

with the Earth at the right angle, just as you've described it and not shown it.

Then 'y' is the side of triangle opposite the angle 'x', and the side adjacent to

the angle 'x' is the unknown distance.

The tangent of an acute angle in a right triangle is

(opposite side) divided by (adjacent side).

So we may write Tangent (x) = y / (unknown distance).

Multiply each side by

(unknown distance) : (unknown distance) (tangent (x)) = y

Divide each side by tangent (x) : Unknown distance = y / tangent (x).

Since he knows the values of both quantities on the right, our intrepid investigator

can repair to his lab at any time and easily calculate the unknown distance.