## Title

Sine and Cosine Rule
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Joined: 20/09/2012 - 08:10
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Sine and Cosine Rule

Okay so i don't really understand these two rules can someone brief me on this. thanks!

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Joined: 07/03/2012 - 18:08
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patem079.310
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Joined: 28/12/2013 - 17:50
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Hopefully This Will Help Form Bitesize

# 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

## When to use it

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.

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.

YZ = 4.40cm?

The angles in a triangle add to 180°.

So angle X was 45°

Now use the formula

# The cosine rule

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:

• a2 = b2 + c2 - 2bc cos A
• or
• b2 = a2 + c2 - 2ac cos B
• or
• c2 = a2 + b2 - 2ab cos C

These formulae can be rearranged to give :

## When to use it

We can use the cosine formula when we are given:

Two sides and an angle.

Three sides

Check whether your formula sheet gives these formulae in both formats. If it does not, you may need to rearrange them yourself.

Question

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

Question

Find the size of angle R.