Question

45 Points!

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

The scientist can use trigonometry to figure out the distance between the Moon and Sun. More specifically, using sine (sin).

Explanation:

Label the triangle first.

- x should be theta

- y would be opposite (o) as it is across/opposite from the side where x is

- the distance between the sun and moon would be hypotenuse (h), as it's opposite of the right angle.

The calculation that has o and h in it's formula is sine. The formula looks like :

Sin(Ф) =
`(o)/(h)`

To solve for the distance between the Sun and Moon, we plug it into the formula and solve

Sin(x) =
`(d)/(y)`

- where d is the distance between the Sun and Moon

hope this helps !! :D

Answer 2

by using pythagoras theorem

Explanation:

the distance between sun and moon is hypoteneous

the distance between earth and sun is perpndicular

and distance between earth and moon is base

we can use,

tanx°=distance betwwen earth and sun/ distance betweenearth and moon

or,

sinx°= distance between earth and sun/ distance between sun and moon

we can use other formulas also same as above 2 examples

Hope ithelps