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 Earth and the sun. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the moon and the sun

Answer 1

Using angle x and it opposite side y, we can compute for the distance from moon to sun which we will denote as d.

now we know from trigonometry, the sin of x(the angle) will be equal to the ratio of it's oppposite side which is y and the hypothenuse which is in this case, the distance of the moon to the sun d or simply:
\[\sin x=y/d\]
multiplying both sides by d we'll have,
\[y=d sinx\]
then we divide both sides by sinx to get
\[d=y/sinx\]
now since we know the value of those two quantities y and sine of x, then we could just plug in those values to get the value of d(distance of moon to sun) right away....