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.

Question

Mathematics

Katelynn Sawyer

18 February, 10:04

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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Answers (1)

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Browning · Answer 1

Using the Law of Sines (sina/A=sinb/B=sinc/C for any triangle)

sinx/y=sin90/d and since sin90=1 we can say that that distance from moon to sun is:

d=y/sinx