The sine rule, cosine rule and area of a triangle
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 7 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Triangles without a right angle
- Labelling
- Area of a triangle
Read the transcript of the teaching part
Last time
Before we start: last time, in Exact trigonometric values and trigonometric graphs, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Triangles without a right angle
SOH CAH TOA only works in a right-angled triangle. But a plot of land, a sail or a mountain path is rarely right-angled. Three more formulas handle any triangle: one for area, the sine rule, and the cosine rule. The skill is choosing the right one, and the clue is in what you are given.
Labelling
Label the angles with capital letters A, B and C, and the sides opposite them with small a, b and c. Side a is across from angle A. This pairing is what every formula uses. Mark the given information on the diagram before choosing a rule.
Area of a triangle
The area of any triangle is a half times a times b times sine of the angle between them. Sides eight and eleven, with an angle of forty between them: half times eighty-eight times sine forty. The area is twenty-eight point two eight square centimetres. The angle must be between the two sides.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Cosine rule · Sine rule.
The whole chapter: Non-Right-Angled Triangles and 3D Trigonometry.
Chapter 26: Further trigonometry
- The sine rule, cosine rule and area of a triangle 6 min
- Three-dimensional problems 5 min
Also for O Level Maths 4024
Which topics come up most in O Level Maths 4024 past papers, counted from every paper since 2004.