Question

All changes saved1. (07.01 MC)The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below:EarthSunMoonA 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 thesetwo measurements to calculate the distance between the Earth and the Sun.

Answer 1

Notice that we can use the trigonometric function tangent to find the distance between the Earth and the Sun with the following expression:

`\begin{gathered} \tan x=(y)/(ES) \\ \Rightarrow ES=(y)/(\tan x) \end{gathered}`

then, if the scientist only have the measure of the distance between the earth and the moon and the angle that forms between the earth and the moon in the sun, we can find out the distance between the Earth and the Sun