Trigonometry

Bendy Quad

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

Hexy-metry

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

Three by One

Stage: 5 Challenge Level: Challenge Level:1

NRICH has always had good solutions from Madras College in St Andrew's, Scotland but the solutions to this problem were truly exceptional.

Far Horizon

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Cubestick

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

Orbiting Billiard Balls

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

Trigonometric Protractor

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

Where Is the Dot?

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

Short Problems

Stage: 4 Challenge Level: Challenge Level:1

A collection of short Stage 4 problems on trigonometry.