# Posts

## Tape Around a Pipe

A long strip of insulating tape is to be wrapped around a hot water pipe. If the width of the strip is w and the diameter of the pipe is d, at what angle must the strip be placed at the edge of the pipe so that no overlapping and no spaces occur?

## Use cos 30 & cos 36 to Get cos 3

Given that cos 30° = √3/2 and cos 36° = (1 + √5)/4. Use formulas for the cosines of sums of angles, differences of angles, etc., to come up with an exact expression (involving radicals) for cos 3°.

## Tangent Circles, Area of Shaded Region A circle centered at A of radius r is externally tangent to a circle centered at B of radius 2r. Tangent lines are drawn from A to the larger circle with points of tangency at D and E respectively. Find the area of the shaded portion of the diagram. ## Angles of a Triangle

It so happens that the triangle whose sides are 4, 5, and 6 has a special property: Its largest angle is twice its smallest angle. Make calculations that support this assertion.