When the moon is exactly half full, the earth, moon, and sun form a right angle. At that time the angle formed by the sun, earth, and moon is measured to be 89.85°. If the distance from the earth to the moon is 240,000 miles, estimate the distance from the earth to the sun. Make sure you show your work step by step.

456,881.78 miles

Explanation:

If there is a right angle among the Earth, moon and the sun, so, that mean that the triangle has a hypotenuse that represent the distance among the Earth and the Sun.

Also, there is another data, the adjacent side of this triangle, the distance among Earth and the Moon.

So with the adjacent side, the right angle, and the hypotenuse, we can work with the geometrical calculation that it is called, cosine.

To obtain the hypotenuse will be:

Cos alfa = adjacent angle over the hypotenuse.

So, to obtain the Hypotenuse: Adjacent side divided into the cosene of 45 º (0.5253)

So, Hyp = CA/cos angle

Hyp = 240, 000 miles / 0.5253 = 456, 881.78 miles

Hope this info is useful