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

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Lesson Worksheet 2

To do this part of the lesson, continue using the Bolt_Circle_1.gsp file you downloaded in the previous section.

DATA: 12 cm bolt circle diameter - 5 bolt pattern

STEP 1: Look at this diagram.

The distance from the lug nut to the center of the circle is called the HYPOTENUSE of the triangle EAX. The HYPOTENUSE is the side opposite the right angle of the triangle.

Measure the length of the HYPOTENUSE

STEP 2: In this situation, it is also half the measure of the bolt circle diameter.

To find the chord length, we need to find the measure of a.

Now, measure <EAX (or <A)?

Also, measure <DAX (or <A)?

What do you notice about these two angles?

STEP 3: We now know the measure of the hypotenuse, and the measure of <A. This is all the information we need to find the chord length. However, we do have to do one more thing.

Highlight the measure of <A. Under the menu Measure, select Calculate.... Find the SIN of <A

STEP 4: Now multiply the SIN of <A and the HYPOTENUSE.

STEP 5: Measure the distance from E to X.

STEP 6: What do you notice about your answer to STEP 4 and 5?

STEP 7: How can you find the chord length from E to D based on your answer to STEP 4.

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