Question

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 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.

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Answer 1

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

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