## 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°.

## Water Poured Into Liter Cube

Water is poured at a constant rate into a one-liter cube near its corner. The water rises to the halfway mark, stops for a moment, and then continues to rise at exactly half its previous rate. The reason is that inside the cube is a hollow cylindrical can that has been attached to the bottom. What are the height and radius of the can? (Recall that a one-liter cube measures 10 cm on each edge.)

## Marvin and Deedee

A: Marvin tied his dog, Deedee, with a rope 10 meters long at an outside corner of his regular hexagonal walled garden having sides of 8 meters. What is the area of ground that Deedee can cover, as determined by the limits of the rope and the walls?

B: Now do the same problem with Deedee tied inside the garden.

## Area Sum of Equilateral Triangles 1 Here are two equilateral triangles; one has side x and the other y. Find the length of the side of an equilateral triangle whose area is the sum of the areas of these two triangles.

## Overlapping Equilateral Triangles

Two congruent equilateral triangles are placed so that their overlap is a regular hexagon. The triangles each have area 24 sq. cm. What is the area of the hexagon?

## Equilateral Octagon Here is a large plywood square. You are going to cut a triangle off of each corner to make a regular octagon. The square is a inches on a side. How many inches should you come in from each corner (x in the picture) so that when you cut off the triangles, all eight sides of the resulting octagon will be equal?