Question

An settler on Mars measures the angle between the star Sero and the star Vega 3 to
be 22.4". If the Mars is approximately 93 million light years from the Sero and Vega 3
is approximately 67 million light years from the Sero (as measured by intergalactic
travelers), how far away is Vega 3 from the Mars?

Answer 1

The distance between Vega 3 and the Mars (MV) illustrates cosine function, and the distance is 29.1 million light years or 142.8 million light years

How to determine the distance between Vega 3 and the Mars?

From the question, we have the following parameters

• Angle between Sero and Vega, Ф = 22.4
• Distance between Mars and Sero, MS = 93 million
• Distance between Vega and Sero, VS = 67 million

See attachment for the illustration of the given parameters.

The distance between Vega 3 and the Mars (MV) is then calculated using the following cosine function

VS² = MS²+ MV² - 2 * MS * MV * cos(Ф)

This gives

4489 = 8649+ MV² -  171.96MV

Subtract 8649 from both sides

MV² -  171.96MV = -4160

Rewrite as:

MV² -  171.96MV + 4160 = 0

Using a graphing tool, we have:

MV = 29.1 and MV = 142.8

Hence, the distance between Vega 3 and the Mars is 29.1 million light years or 142.8 million light years

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