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?
NRICH has always had good solutions from Madras College in St Andrew's, Scotland but the solutions to this problem were truly exceptional.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?
An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.
A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?
A collection of short Stage 4 problems on trigonometry.