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Expert: - 9/29/2009


Question
The figure shows a circular piece of sheet metal of diameter 40 centimeters. The sheet contains 12 equally spaced bolt holes. Determine the straight-line distance between the centers of two consecutive bolt holes. (θ = 30°, x = 34 cm.)

Answer
I will assume the bolt holes are around in a circle.

Determin the distance from the center for each hole.

For two holes that are adjacent to each other, construct a triangle.

The inside angle on this triangle would be 360°.

Since there are 12 bolts, there is 30° between each pair.

The line between each adjacent pair can be used to form a triangle with the middle.

The 30° angle in the middle can be cut in half,
making two right triangles with the right angle being between the two.

The measure of the inside angle is 15°.

The length of the line between them is twice the outside edge of this triangle.
I'll call the length of this edge 2L, so the triangle has a side of length L.
It is known that tan(15°) = L/D, where D is the distance out.

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