Questions: Pythagoras and trigonometry
Pick a question type. Each time you get new numbers. Free ones are marked free.
Pythagoras' theorem
- Find the hypotenuseCalculate, 3 marks, free
- Find a shorter sideCalculate, 3 marks, free
- Pythagoras with whole-number sidesWork out, 3 marks, free
- Is it a right angle?Work out, 3 marks, free
- Distance between two pointsCalculate, 3 marks, free
- A ladder against a wallWork out, 6 marks, free
- Across a rectangleWork out, 5 marks, free
- Height and area of an isosceles triangleWork out, 5 marks, free
- Which equation is Pythagoras?Choose, 1 mark, free
Sin, cos and tan for sides
- Name the sidesChoose, 3 marks, free
- Choose the ratio, then find the sideWork out, 4 marks, free
- A shorter side from the hypotenuseCalculate, 3 marks, free
- A side with tanCalculate, 3 marks, free
- Find the hypotenuse with trigonometryCalculate, 3 marks, free
- Heights and distances on a slopeCalculate, 4 marks, free
- sin, cos and tan as fractionsWrite down, 3 marks, free
- Two right-angled trianglesCalculate, 5 marks, free
Finding angles, elevation and bearings
- Find an angleCalculate, 3 marks, Plus
- Which calculation gives the angle?Choose, 1 mark, Plus
- The angle of a slopeCalculate, 3 marks, Plus
- An angle of elevation from eye levelCalculate, 4 marks, Plus
- A height from an angle of elevationCalculate, 3 marks, Plus
- An angle of depressionCalculate, 3 marks, Plus
- Distance and bearing from a journeyWork out, 5 marks, Plus
- How far east and how far northWork out, 4 marks, Plus
- Angles of an isosceles triangleCalculate, 4 marks, Plus
- Spot the calculator slipChoose, 1 mark, Plus
- Is the ladder at a safe angle?Work out, 4 marks, Plus
Exact values and 3D
- Exact values of sin, cos and tanWrite down, 2 marks, Plus
- Calculate with exact valuesWork out, 2 marks, Plus
- Exact lengths in 30°, 45° and 60° trianglesWork out, 3 marks, Plus, Higher tier
- An angle from an exact valueWrite down, 2 marks, Plus
- Pythagoras with a surd answerWork out, 3 marks, Plus, Higher tier
- The diagonal of a cuboidCalculate, 3 marks, Plus, Higher tier
- The angle between a diagonal and a planeCalculate, 4 marks, Plus, Higher tier
- Height and angle in a pyramidCalculate, 7 marks, Plus, Higher tier
- A mast in the corner of a fieldCalculate, 5 marks, Plus, Higher tier
The sine and cosine rules
- The sine rule for a sideCalculate, 3 marks, Plus, Higher tier
- Sine rule after the third angleCalculate, 4 marks, Plus, Higher tier
- The sine rule for an angleCalculate, 3 marks, Plus, Higher tier
- The cosine rule for a sideCalculate, 3 marks, Plus, Higher tier
- The cosine rule for an angleCalculate, 3 marks, Plus, Higher tier
- Area = ½ab sin CCalculate, 2 marks, Plus, Higher tier
- Working back from an areaCalculate, 3 marks, Plus, Higher tier
- Which rule?Choose, 1 mark, Plus, Higher tier
- Two boats on bearingsWork out, 4 marks, Plus, Higher tier
- A triangular fieldWork out, 6 marks, Plus, Higher tier
- How many triangles?Choose, 1 mark, Plus, Higher tier
- Sine rule, then the areaWork out, 6 marks, Plus, Higher tier
- Show that an angle is right to 1 d.p.Show that, 3 marks, Plus, Higher tier
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