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 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

I think you need the diagram

Answer 2

y= Distance between earth and sun
Secant x= Distance between moon and sun/y
y*secant x= distance between moon and sun

Answer 3

well you can use a trig ratio... which one would you choose

Answer 4

MissSunshine - y = Earth Moon distance

Answer 5

oh ok well wouldnt i use the equation sin(x) = d/y

Answer 6

y= Distance between earth and moon
Secant x= Distance between moon and sun/y
y*secant x= distance between moon and sun

Answer 7

Of course

Answer 8

Plug it in; show us your explanation @Moo_Moo17

Answer 9

in the triangle shown y is the opposite side to angle x

and the distance earth to sun is the adjacent side

so you have the opposite side, need to find the adjacent side using an angle x

which ratio...

I wouldn't use secant

Answer 10

How's this?
tangent (x degrees) = opposite / adjacent
tangent (x degrees) = Earth Moon Distance / Earth Sun Distance

Answer 11

Moo_Moo17 - What would you do next?

Answer 12

This is the last sentence from my previous answer
tangent (x degrees) = Earth Moon Distance / Earth Sun Distance

So, if you can solve for Earth Sun Distance, that should be the last step in your answer.
So, what is the Earth Sun distance?