Angles, Triangles and Trigonometry - June 2007, Stage 2&3

Problems

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How Safe Are You?

Stage: 2 Challenge Level: Challenge Level:1

How much do you have to turn these dials by in order to unlock the safes?

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Six Places to Visit

Stage: 2 Challenge Level: Challenge Level:1

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

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Number the Sides

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

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

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Dotty Circle

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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Round and Round and Round

Stage: 3 Challenge Level: Challenge Level:1

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

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Can You Explain Why?

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you explain why it is impossible to construct this triangle?

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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?