Question

A 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 these two measurements to calculate the distance between the Earth and the Sun.

Answer 1

tan =opposite/adjacent

In this case: tan =X , opposite=Y and adjacent= D

tan(x)=Y(opposite) /D(adjacent)

All terms in the equation are known except for 'D the distance'.

So the distance between the earth and the sun indicate by the symbol 'D' is equal to: y/tan(x)

Answer 2

Let the distance between the earth and the sun be denoted as 'z'.
From the trigonometric rules:
tan(theta)=opposite/adjacent

In this case: theta=x , opposite=y and adjacent=z

tan(x)=y/z
All terms in the equation are known except for 'z'.
therefore the distance between the earth and the sun denoted by the symbol 'z' is equal to: y/tanx