Geometry help! Please!!

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 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

Hi Billy J.

The following Trigonometric functions; sine, cosine and tangent apply to the sides and angles in every right triangle

For angle x

The cosine of angle x is Adjacent side, which is side y divided by the hypotenuse, or the longest side of the right triangle, in your drawing the longest side is the distance between the sun and the moon

For angle x

y/(cosine x) = distance between the sun and the moon

You can look up the Trigonometric Function typically used with Right Triangles in your text or on the internet.

They are usually referred to Sin, Cos, and Tan when applied to a Right Triangle

Sin = Side Opposite of the given angle/(Hypotenuse)

Cos = Side Adjacent to the given angle/(Hypotenuse)