The moon forms a right triangle with the earth and the sun during one of its phases, as shown below: a right angle triangle is shown with the earth at the right angle. the acute angle between the line joining the earth and the sun and the sun and the moon is x degrees. the distance between the earth and the moon is y. 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.

if you explain the the question more correctly i might be able to answer this better

step-by-step explanation:

9x

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)