Sine rule and cosine rule

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?

How far should the roof overhang to shade windows from the mid-day sun?

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

Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.

Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.

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

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

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.

Explore the geometry of these dart and kite shapes!

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.