Question

The moon forms a right triangle with the Earth and the Sun during one of its phases, as shownbelow:EarthSunуMoonA scientist measures the angle x and the distance y between the Earth and the moon. Usingcomplete sentences, explain how the scientist can use only these two measurements to calculatethe distance between the Earth and the Sun. (10 points)

Answer 1

The moon, sun, and the earth form a right angle triangle

The distance between the Moon and the Earth is the opposite side it is opposite the angle x measured by the scientist which is y

The distance between the Sun and the Earth is called the adjacent side

To calculate the distance between the Sun and the Earth, the scientist will trigonometry ratio for the tangent of an angle given as

`\begin{gathered} \tan x=(opposite)/(adjacent) \\ \end{gathered}`

Hence the distance between the Earth and the Sun will be calculated by dividing the distance between the moon and Earth by the tangent of the angle x

Let the distance between the Earth and Sun be Z

Hence we have

`z=(y)/(\tan x^0)`