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

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°