Okay so i don't really understand these two rules can someone brief me on this. thanks!
Try this page http://revisionworld.com/gcse-revision/maths/trigonometry/sine-and-cosine-rule
We can use the sine rule to find the size of an angle or length of a side.
The sine rule is:
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.
Find the size of angle R.
R = 25.4°
Using the sine we can write:
Multiplying both sides by 4, we get
SO R = inv sin(0.4293)
R = 25.4° (1dp)
Remember: Use the formula which has the unknown at the top of the fraction.
Find the length of YZ.
YZ = 4.40cm?
The angles in a triangle add to 180°.
So angle X was 45°
Now use the formula
We can use the cosine formula to find the length of a side or size of an angle.
For a triangle with sides a,b and c and angles A, B and C the cosine rule can be written as:
These formulae can be rearranged to give :
We can use the cosine formula when we are given:
Two sides and an angle.
Check whether your formula sheet gives these formulae in both formats. If it does not, you may need to rearrange them yourself.
Find the length of BC.
Did you get 4.86cm? If so, well done.
If not, remember to use the formula:
a2 = b2 + c2 - 2bc cos A
Substitute the values into the formula.
a2 = 72 + 32 - 2 × 3 × 7 cos 35
a2 = 58 - 42 cos 35
a2 = 23.5956
a = 4.86cm
R = 31.8°
You need to use the formula:
R = inv cos 0.8497
Therefore, R = 31.8°
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