Uniform circular motion, earth's rotation

[bulbasaur88]

The Earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. Assuming the Earth is a sphere with a radius of 6.38 x 10⁶ m, determine the speed and centripetal acceleration of a person situated at a latitude of 30.0 degrees north of the equator.

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My Attempt
I understand that we are looking at a cross section of the Earth at latitude 30.0 degrees north of the equator. I also understand how to get to the answer:

Given
T = 1 day = 86, 400 seconds

1. Find velocity from V = (2pi*r)/T

2. Take the velocity from the previous equation and plug into to find a_c:
a_c = v²/r

I know that the radius at 30 degrees north of the equation is r_earthcos30...My question is: WHY is the radius r_earthcos30? I cannot see the geometry behind this conclusion! :(

 

[gneill]

The radius of import is the distance to the axis of rotation. For a latitude 30.0° N, how would you calculate that distance?

 

[bulbasaur88]

Wow - this was a very silly question to ask on my part. When I saw the answer, it literally slapped me in the face. I can't believe I didn't see that...Thank you gneill.