With this trigonometry i just need an explanation, this is the only question i need with.

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 sun and the moon is y.
a scientist measures the angle x and the distance y between the sun 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 moon.

Step-by-step explanation:

There are an awful lot of words, but it boils down to something that can be handled.

He measures x which is an angle

He measures y which is a distance. Not only that it is also the hypotenuse of a right triangle.

He would like to know z which is the distance from earth to moon.

The relationship he should use is sin(x) = opposite / hypotenuse

sin(x) = z/y   Multiply both sides by y

y * sin(x) = z/y * y

z = y * sin(x)

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct

x= 3^y

step-by-step explanation: