Question

The moon forms a right triangle with the Earth and the sun during one of its phases, as shown below.

A scientist measures the angle x and the distance y between the sun 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 moon.

Answer 1

Earth Sun distance (or Moon Sun distance) = 93,000,000 miles
sine x° = Earth Moon Distance / 93,000,000
Earth Moon Distance = sine x° * 93,000,000

(I already know the Earth Moon distance = 240,000 miles)
So the sine of x° = 240,000 / 93,000,000
= 0.0025806452
angle x = arc sine 0.0025806452
angle x = 0.14786 Degrees