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Broad Topics >

Pythagoras and Trigonometry > Sine rule & cosine rule

##### 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?

##### Age 14 to 16 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Explore the geometry of these dart and kite shapes!

##### Age 14 to 16 Challenge Level:

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.

##### 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.

##### Age 14 to 16 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

##### Age 14 to 16 Challenge Level:

Given a square ABCD of sides 10 cm, and using the corners as
centres, construct four quadrants with radius 10 cm each inside the
square. The four arcs intersect at P, Q, R and S. Find the. . . .