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## anonymous 2 years 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.

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1. anonymous

|dw:1394916038880:dw|

2. anonymous

|dw:1394916191485:dw|

3. anonymous

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

4. anonymous

Please explain more

5. anonymous

Never mind I worked it out

6. anonymous

But, thank you for the help

7. anonymous

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. anonymous

Thanks

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