Question

Arc Length Stuff: Have you ever wondered what the circumference of the Earth is? Well, at the Equator, the distance around is about 25000 miles (assuming the Earth is a sphere). What if you wanted to know the distance around at any latitudinal location? For instance, if you traveled along the Arctic Circle all the way around, how many miles would you actually go? This problem is all about latitudinal travel at various degrees of latitude:
Let C be the distance around the Earth at latitude location θ. Find a formula that will calculate C for any value of θ. Then use this formula to find the following distances (it should also work at the Equator, yes…show this):
Around the Earth at the Tropic of Cancer/Capricorn (23.5˚ latitude)
Around the Earth at the Arctic/Antarctic Circle (66.5˚ latitude)
Around the Earth at the North/South Pole (90˚ latitude)
Around the Earth at Portland’s latitude (45.5˚ latitude)
At what latitude(s) will the distance around the Earth be 5000 miles? How about 15000 miles? Your results should be in units of degrees(◦) latitude.

This is really confusing me. Can someone help please??

Answer 1

C = 25000 cos(θ)

plug in the various values of θ to find the corresponding C

Answer 2

draw a diagram. It is clear that at latitude θ, the distance around the earth is 25000 cosθ.

So, the circumference at the arctic circle is 25000 cos 66.5˚ = 9969 miles

So, for a circumference of, say, 5000 miles, you want

cosθ = 5000/25000 = 0.2
θ = 78.46˚

Answer 3

Suggest Sea Scouts :)