Maths (school) · Part 06
Pythagoras and trigonometry
Right-angled triangles, sine, cosine and tangent, and the sine and cosine rules.
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- Pythagoras' theoremIn a right-angled triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides: a^2 + b^2 = c^2.
- Distance between two pointsYou can use Pythagoras on a coordinate grid. The horizontal and vertical gaps between two points make the short sides of a right-angled triangle.
- Sine, cosine and tangentThree ratios linking an angle in a right-angled triangle to its sides: sin = opposite / hypotenuse, cos = adjacent / hypotenuse, tan = opposite / adjacent.
- Finding a missing sidePut the angle and known side into the correct ratio, then rearrange to get the unknown side.
- Finding a missing angleUse the inverse button (sin^-1, cos^-1 or tan^-1) on your calculator to turn a ratio back into an angle.
- Exact trigonometry valuesSome angles have neat values you can write without a calculator: sin 30 = 1/2, cos 60 = 1/2, tan 45 = 1.
- Angles of elevation and depressionThe angle of elevation is measured upwards from the horizontal. The angle of depression is measured downwards from the horizontal.
- Sine ruleFor any triangle, side a over sin A equals side b over sin B. It links sides to the angles opposite them.
- Cosine ruleFor any triangle, c^2 = a^2 + b^2 - 2ab cos C. It finds a side when you know two sides and the angle between them.