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

Is that helpful enough, or you want me to explain more?

Answer 2

Please explain more

Answer 3

Never mind I worked it out

Answer 4

But, thank you for the help

Answer 5

Angles in every triangle always add up to 180 degrees.
So you have 2 angles out of 3, which means you can get the third one.
Let's call it m, so m=180-90-x

Now sine rule:
\[\frac{ a }{ \sin A }=\frac{ b }{ \sin B }=\frac{ c }{ \sin C }\]
Small letters are always used for the sides, and capitals for the angles.
Which means \[\frac{ y }{ \sin m } = \frac{ distance \between earth and sun }{ \sin 90 }\]

Answer 6

Thanks