Three points A, B and C lie in this order on a line, and P is any
point in the plane. Use the Cosine Rule to prove the following
Age 14 to 16 Challenge Level:
Draw a right-angled triangle.
Click and drag near the centre of the protractor to move its centre
over a vertex of a triangle (not at the right angle).
Click and drag on the inner circle to rotate it until the blue dot
aligns with one of the adjacent sides.
Click and drag the blue dot until it aligns with the
What do the numbers refer to?
Click and drag the edge of the protractor to change its
Why don't the numbers change?
How might this protractor be useful for finding the lengths of
sides of different triangles?
What do you notice about the numbers when the protractor is
placed over each of the two acute angles? Can you explain what you
What is the connection between the "lengths" of the two
adjacent sides and the "length" of the hypotenuse?
Do these things remain the same for any triangle? Can you
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.