Question

The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below:

Answer 1

Answer:

The distance between the Earth and the Moon is equal to the distance between the Sun and the Moon multiplied by the sine of angle x

Step-by-step explanation:

Let

EM -----> the distance between the Earth and the Moon.

y -----> the distance between the Sun and the Moon.

we know that

In the right triangle of the figure

The sine of angle x is equal to divide the opposite side to angle x (distance between the Earth and the Moon.) by the hypotenuse ( distance between the Sun and the Moon)

so

sin(x)=EM/y

Solve for EM

EM=(y)sin(x)

therefore

The distance between the Earth and the Moon is equal to the distance between the Sun and the Moon multiplied by the sine of angle x