Can you explain why it is impossible to construct this triangle?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

What is the total area of the first two triangles as a fraction of the original A4 rectangle? What is the total area of the first three triangles as a fraction of the original A4 rectangle? If. . . .

Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.