SOLUTION: distance to the sun when the moon is exactly half full, the earth, the moon and the sun from a right angle. At the time the angle formed by the sun, earth, and the moon is measured

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Question 1165117: distance to the sun when the moon is exactly half full, the earth, the moon and the sun from a right angle. At the time the angle formed by the sun, earth, and the moon is measured to be 89.85 degrees. If the distance from the earth to the moon is 240,000mi, estimate the distance from the earth to the sun.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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distance to the sun when the moon is exactly half full, the earth, the moon and the sun from a right angle.
At the time the angle formed by the sun, earth, and the moon is measured to be 89.85 degrees.
If the distance from the earth to the moon is 240,000mi, estimate the distance from the earth to the sun.
:
In the right triangle formed we can use the cosine of 89.85 degrees where hypotenuse is the distance (d) to the sun
and the 240k is the side adjacent (dist to the moon from the earth)
Cos(89.15) = 240000%2Fd
d = 240000%2Fcos%2889.85%29
d = 91,673,352 mi