About this topic
Before you begin
Solve right and non-right triangles in G2 Mathematics, checking sine-rule alternatives, bearings and three-dimensional projections.
Learning goals
- Use and justify Pythagoras’ theorem
- Calculate a hypotenuse from two perpendicular lengths
- Calculate a shorter side from a hypotenuse and another side
- Test the Pythagorean equality using the longest side
- Choose a right-triangle ratio and calculate a side
- Choose a right-triangle ratio and calculate an acute angle
- Calculate a trigonometric height difference and the height from its reference
- Use trigonometric ratios in right-angled triangles
- Calculate a side from opposite angle-side pairs using the sine rule
- Find every possible triangle angle from sine-rule givens
- Calculate the opposite side from two sides and their included angle
- Calculate an acute or obtuse angle from three triangle sides
- Calculate triangle area from two sides and their included angle
- Use sine and cosine rules for general triangles
- Turn a two-leg bearing journey into a triangle and find the direct distance and bearing
- Identify a projection in a cuboid or right pyramid and calculate its angle to a plane
- Calculate the requested distance and bearing in a two-leg journey
- Calculate the angle between a line and a plane in a cuboid or right pyramid
Syllabus statements covered
- Use of Pythagoras’ theorem
- Determining whether a triangle is right-angled given the lengths of three sides
- Use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles
- Extending sine and cosine to obtuse angles
- Use of the formula ½ab sin C for the area of a triangle
- Use of sine rule and cosine rule for any triangle
- Problems in two and three dimensions including those involving angles of elevation and depression and bearings Sine/cosine rules and two-/three-dimensional problems (including elevation, depression and bearings) are tested only in Paper 2 Section B.
- Use of Pythagoras’ theorem
- Determining whether a triangle is right-angled given the lengths of three sides.
- Use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles
- Extending sine and cosine to obtuse angles
- Use of the formula ½ab sin C for the area of a triangle
- Use of sine rule and cosine rule for any triangle
- Problems in two and three dimensions including those involving angles of elevation and depression and bearings
Choose a lesson
Work through them in order.
- Not startedPythagoras and its converseNextUse the side opposite a right angle and test whether three lengths form a right triangle.
- Not startedRight-triangle sine, cosine and tangentNextName sides relative to the chosen acute angle and choose a ratio using the available quantities.
- Not startedSine rule, cosine rule and triangle areaNextChoose a rule from the given sides and included angles, and check ambiguous sine-rule solutions.
- Not startedBearings and three-dimensional trianglesNextDraw the relevant plane triangle and keep horizontal projections distinct from sloping lengths.
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