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twopack98 Group Title

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.

  • 4 months ago
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  1. twopack98 Group Title
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    |dw:1394916038880:dw|

    • 4 months ago
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    |dw:1394916191485:dw|

    • 4 months ago
  3. nickersia Group Title
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    Is that helpful enough, or you want me to explain more?

    • 4 months ago
  4. twopack98 Group Title
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    Please explain more

    • 4 months ago
  5. twopack98 Group Title
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    Never mind I worked it out

    • 4 months ago
  6. twopack98 Group Title
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    But, thank you for the help

    • 4 months ago
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    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 \[\frac{ y }{ \sin m } = \frac{ distance \between earth and sun }{ \sin 90 }\]

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    Thanks

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