Final answer:
To find the approximate distance between Mars and Jupiter, we can use the Law of Cosines and the given distances and angle. By substituting the values into the formula, we find that the approximate distance is approximately 553 million miles.
Step-by-step explanation:
To find the approximate distance between Mars and Jupiter, we can use the included angle and the distances given.
First, we can use the Law of Cosines to find the distance between Jupiter and Mars. The formula for the Law of Cosines is: c^2 = a^2 + b^2 - 2ab * cos(C), where c is the distance between Jupiter and Mars, a is the distance between Earth and Jupiter (391 million miles), b is the distance between Earth and Mars (160 million miles), and C is the included angle (118°).
Using this formula, we can substitute the given values and solve for c:
c^2 = (391 million miles)^2 + (160 million miles)^2 - 2(391 million miles)(160 million miles) * cos(118°)
c^2 ≈ 152,564 + 25,600 + 126,976
c^2 ≈ 305,140
c ≈ √305,140 ≈ 553 miles
Therefore, the approximate distance between Mars and Jupiter at that time was approximately 553 million miles.