Consumer reports would like to conduct a hypothesis test to determine if the average

if someone is on the moon, and measures the angle from the earth to the sun, then that angle is x (some unknown number). if we let y be some unknown distance from the earth to the sun, and z be another unknown distance from the moon to the sun, then we can tie all of these variables together.

we do so by using the sine ratio which says that sin(angle) = opposite/hypotenuse. in our case, x is the angle in question, y is the opposite or side furthest from angle x, and z is the hypotenuse. the hypotenuse is always the longest side opposite the 90 degree angle.

so using those facts, we can go from sin(angle) = opposite/hypotenuse to the new equation sin(x) = y/z.

now multiply both sides by z

sin(x) = y/z

z*sin(x) = y

then divide both sides by sin(x) to isolate z

z*sin(x) = y

z = y/( sin(x) )

if we knew the numeric values for x and y, then we could compute the actual value of z to find the actual distance from the moon to the sun. since we don't know these values, we leave that last equation as is.