Question

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

A right angle triangle is shown with the Earth at the right angle. The acute angle between the line joining the Earth and the Sun and the Sun and the moon is x degrees. The distance between the Sun and the moon is y.

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.

Answer 1

@phi

Answer 2

You are given x and y, and you need to explain how to find d, the distance between the Earth and the moon, using only x and y.

Answer 3

We have a right triangle, so we can use trigonometry of triangles.
Our reference angle is x.
For angle x, which leg is the adjacent leg, and which leg is the opposite leg?

Answer 4

Hint:
adjacent = next to
opposite = across from

Answer 5

Do you see which sides are the legs and the hypotenuse?

Answer 6

You know angle x.
You know side y, the hypotenuse.
You need side d, the opposite leg.
Which trig function relates the opposite leg and the hypotenuse?