Bolt Circle Diameter Module:
Finding the Bolt Circle Diameter from Chord Length

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## Problem Description

In this module students will,

investigate trigonometric ratios
determine the bolt circle diameter of a tire given it's chord length and vice versa
investigate the connection between the circumference of a circle and PI using many sided polygons

A problem often seen in automotive technology is determining the bolt circle diameter of a tire.

The above diagram shows a typical bolt pattern consisting of 5 lug nuts. A lug nut is demonstrated by each of the small circles that is around the bigger circle. Once either the chord length or the bolt circle diameter is known, the other can be found.

To find either measurement, it is necessary to use trigonometry. Trigonometry is the study of triangles and their properties so the first part of this lesson will be to learn a little about triangle ratios and their part in this problem.

If needed a short tutorial is provided if the student is unfamiliar with Geometer's Sketchpad.

Otherwise, Continue the Lesson Worksheet 1.