The moon forms a right triangle with the earth and the sun during one of its phases, as shown below: a scientist measure the angle x and the distance y between the earth an 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.

He uses trigonometry.  In a right angled triangle, which we have here, we use one of the trig ratios sine, cosine or tangent to find  lengths of sides and/or measures of angles. The distance between the Moon and the Sun in this diagram is the hypotenuse of the triangle. We only need to know the measure of one angle ( other than the right angle) and another side to find this.
Here we use the cosine  :- cos x = adjacent / hypotenuse  so the hypotenuse = adjacent / cos x. = y / cos x.  We know what x and y are so its easy to find the hypotenuse.