Flashcards · 7 cards

Sine & cosine rules

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Rule
How do you label a triangle for the sine and cosine rules?
Answer
Side $a$ faces angle $A$ , side $b$ faces angle $B$ , side $c$ faces angle $C$ .
Sides and opposite anglesSide a faces angle A, and so on
From the lesson: The sine rule and the cosine rule
Know it
The sine rule?
Answer
$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$ .
From the lesson: The sine rule and the cosine rule
Know it
The cosine rule?
Answer
$c^2 = a^2 + b^2 - 2ab\cos C$ . For an angle: $\cos C = \dfrac{a^2 + b^2 - c^2}{2ab}$ .
From the lesson: The sine rule and the cosine rule
Know it
When do you use the sine rule, and when the cosine rule?
Answer
Sine rule: you know a side and the angle opposite it. Cosine rule: two sides and the angle between them, or all three sides.
From the lesson: The sine rule and the cosine rule
Know it
What is $\cos 120^\circ$ , and what does it do in the cosine rule?
Answer
$-\frac12$ . So $-2ab\cos 120^\circ = +ab$ : the side opposite an obtuse angle comes out longer.
From the lesson: The sine rule and the cosine rule
Rule
The bisector of angle $M$ in triangle $MNO$ meets $NO$ at $P$ . How does it divide $NO$ ?
Answer
In the ratio of the other two sides: $\dfrac{NP}{PO} = \dfrac{MN}{MO}$ .
The angle bisectorThe longer side next to M gets the longer piece
From the lesson: The sine rule and the cosine rule
Which method?
WAEC 2017 · Paper 2 · Q9 (a)
An aeroplane flies 100 km from town $A$ on a bearing of $330^\circ$ to town $B$ . It then flies 300 km due west to town $C$ . (i) Illustrate this information in a diagram. (ii) Calculate the: (I) distance between $A$ and $C$ , correct to two decimal places; (II) bearing of $C$ from $A$ .
How do you find the angle at $B$ ?
Answer
At $B$ , the bearing back to $A$ is $330^\circ - 180^\circ = 150^\circ$ and on to $C$ is $270^\circ$ , so $\angle ABC = 120^\circ$ . Then the cosine rule gives $AC$ .
From the lesson: Bearings with any triangle Try the question