Part 06 · Pythagoras and trigonometry · Card 8 of 9
Sine rule
For any triangle, side a over sin A equals side b over sin B. It links sides to the angles opposite them.
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Analogy
Like a fair-trade rule: each side always has the same ratio to its opposite angle.
Example
A = 30, a = 7, B = 50
b / sin 50 = 7 / sin 30b = 7 x sin 50 / sin 30= 7 x 0.766 / 0.5= 10.7
In practice
Navigators use it to find distances when no angle is a right angle.
Practice
Flashcards
- Write the sine rule.a / sin A = b / sin B.
Questions people ask
When do you use the sine rule?
Use it when you know an angle and the side opposite it, plus one more angle or side. You need a matching pair. If you only know two sides and the angle between them, you need the cosine rule instead.
How does the sine rule go when finding an angle?
Flip the rule so the sines are on top: sin A / a = sin B / b. Substitute what you know, rearrange to find sin of the unknown angle, then use the inverse sine button on your calculator to find the angle.