5. how do the number of miles between longitude lines at the equator compare to the same lines near the poles?

Explanation given under.

Explanation:

A map is a two-dimensional representation of the earth and its features on the globe so, to represent this, the latitude and longitudes are imaginary lines that separate the northern and southern ends of the earth being divided the Geographic equator at 0 degrees.  These alt longs create a type of grid that gives to the coordinate system of the earth. Like the circle, the latitude and longitudes are measured in degrees, minutes and seconds. The equator being in 360 degrees, the longitude values ranging from 180 degrees W to 180 E. As all longitudinal lines are equal at all places, they always cover the same distance as 60 miles. In contrast, the degrees of Latitude vary as near equator the degree of latitude is 60 miles but as you approach the poles the distance becomes zero. The range of latitude then is  -90 (S) to +90 (N) degrees i.e tropic of cancer 23.5N, tropic of Capricorn 23.5S, and the Arctic and Antarctic circles at 66.5 N, S.

I'm pretty sure there's a geometry rule for   anyways, if the triangle is equilateral, and the circle is circumscribed, the circle is outside of the triangle.  to find the area, you need the radius.  the radius should be a straight line from the center of the triangle to any of it's points.  draw lines from the center of the circle to each of the triangle points.  draw three more lines from the center to the middle of the sides of the triangle.  you should now have six separate 30-60-90 triangles inside of your original triangle. use your 30-60-90 rules to solve for the radius, then the circumference.