Which ratio is smaller 4: 2 or 5: 4

If tan2a=cot(a+60), find the value of a, where 2a is an acute angle

What is the distance between a and b? round your answer to the nearest tenth. a coordinate plane is shown. point a is located at negative 1, 5, and point b is located at 4, 1. a line segment connects the two points.

Meghan has created a diagram of her city with her house, school, store, and gym identified. a. how far is it from the gym to the store? b. meghan also wants to walk to get some exercise, rather than going to the gym. she decides to walk along arc ab. how far will she walk? round to 3 decimal places.