Sine rule and cosine rule

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation of Pythagoras' Theorem.