Sine rule and cosine rule

problem

Raising the Roof

Age

14 to 16

Challenge level

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

Biggest Bendy

Age

16 to 18

Challenge level

Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?
problem

Cyclic Triangles

Age

16 to 18

Challenge level

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.
problem

Xtra

Age

14 to 18

Challenge level

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.
problem

Calculating With Cosines

Age

14 to 18

Challenge level

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?
article
The Dodecahedron Explained

What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?