## twopack98 one year ago 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.

1. twopack98

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2. nickersia

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3. nickersia

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

4. twopack98

5. twopack98

Never mind I worked it out

6. twopack98

But, thank you for the help

7. nickersia

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 $\frac{ y }{ \sin m } = \frac{ distance \between earth and sun }{ \sin 90 }$

8. twopack98

Thanks