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## Homework Statement

I'm trying to create a clock face in Python and cant quite figure out where I'm going wrong.

Statement: For a clock of radius 100 units, what will be the distance between two adjacent numbers?

If a turtle walks along the path joining two adjacent numbers, by what angle will it have to turn at every number.

## Homework Equations

Trigonometric identities for tan / sin / cos.

Sum of angles in a polygon = 360 degrees

## The Attempt at a Solution

An analog clock has numbers from 1 to 12, with an origin at the center.

Consider a figure where two adjacent numbers are joined by a straight line (say nos. 1 and 2)

Let the distance between the origin and the numbers 1 and 2 be 100 (the nos 1 and 2 are equidistant from the origin).

The angle made at the center is 360/12 = 30 degrees for a 12 sided regular polygon.

This means the triangle ABC (vertices at the origin, nos 1 and 2) is an isosceles triangle with angles 30, 75 and 75 degrees respectively.

Dropping a perpendicular from vertex B to point D on side AC results in an angle ABD of 60 degrees. Which implies that perpendicular BD is of length 100 * cos 60.

This then implies that side BC is of length [tex]\frac{100*cos60}{sin75}[/tex].

The angle that the turtle will have to turn at every such vertex (1,2,3...12) is 30 degrees.

However, I think the length BC is incorrect.

Can someone please confirm?