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Before starting this section, you should have already revised trigonometry and Pythagoras' theorem.
We are now going to extend trigonometry beyond right-angled triangles and use it to solve problems involving any triangle.
The sine rule
We can use the sine rule to find the size of an angle or length of a side.
The sine rule is:
or
We can use the sine rule when we are given:
Two sides and an angle opposite to one of the two sides.
One side and any two angles.
- Question
Find the size of angle R.
- Answer
R = 25.4°
Using the sine we can write:
Multiplying both sides by 4, we get
= 0.4293...SO R = inv sin(0.4293)
R = 25.4° (1dp)
Remember: Use the formula which has the unknown at the top of the fraction.
- Question
Find the length of YZ.
- Answer
YZ = 4.40cm?
The angles in a triangle add to 180°.
So angle X was 45°
Now use the formula
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