Pythagoras' Theorem & Trigonometry

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

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

There are many different methods to solve this geometrical problem - how many can you find?

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