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.

Step-by-step explanation:

The Earth, Sun and Moon form a right triangle.

By the definition of cosine in a right triangle we can write that  

cos x ° = adjacent side /hypothenuse  = y/ distance Moon Sun

Since we measured the angle x, and the distance y we can use algebra to find the unknown distance between the moon and the Sun.

distance Moon Sun = y/cos x°

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3