SohCahToa
We use SohCahToa to figure out an unknown angle or side in a right angled triangle. In questions, you will see a right angled triangle and have either two sides given (so you can calculate an angle), or an angle and a side (so you can calculate another side).
For example:

To find angle x we would use SohCahToa, specifically ‘Toa’. This is because: It is a right angled triangle Two sides have been given: the opposite, and the adjacent
We know the opposite and adjacent sides to this angle therefore tan x = opposite / adjacent = 5/7. To find x by itself we then use the inverse tan (tan-1) function on our answer to give 35.5
Sine rule
The sine rule can be arranged to calculate angles or lengths and is as follows:

Where a, b, and c are sides, and A, B, and C are their respective opposite angles. This can be used for any type of triangle. We can use this rule when we are given two sides and an angle opposite one of the sides (to calculate an angle) or when we have one side and any two angles (to calculate a side). Therefore in a question look for any type of triangle and this information.
For example:

To find angle x we need to use the Sine rule. This is because:
It is a triangle (in this case not a right angled triangle)We have been given two sides and an angle opposite to one of those sides.
Therefore using SinA/a = SinB/b, we can substitute in the given values to give sinx/4 = sin74/9.
We can then rearrange this to make sin x the subject: sinx = 4 x sin75 / 9. If we type this into a calculator it gives 0.4293. We can then apply the inverse sin (sin-1) function to isolate x giving the value of 25.4°.
Cosine rule
The cosine rule can be arranged to calculate angles or lengths and is as follows:

Where a, b, and c are sides, and A, B, and C are their respective opposite angles. The cosine rule can also be used in any type of triangle. We can use this rule when three sides are known (to calculate an angle), or when two sides and the angle between them are known (to calculate a side. Therefore in a question look for any type of triangle and this information.
For example:

To find side x we need to use the cosine rule. This is because:
It is a triangle (in this case not a right angled triangle)We have been given two sides and an angle between those sides.
Note that if we tried to use the sine rule here it wouldn’t work! We don’t have opposite angles for either of the sides we are given.
Using the cosine rule, we can substitute in the values given to give us the answer. Therefore x2 = 32 + 72 - 2 x 3 x 7cos35. We then have to square root the answer to give us x because right now we have a value for x2. This gives us an answer of 4.86 cm.

X^2 - 4y = -8 y=3

Related Maths GCSE answers

Solve the inequality 5x^2 + x - 3 = 1

How can you differentiate when to use SohCahToa and when to use the sine/cosine rules?

How do you find the mean of 5 values?

Factorise 3x^3y^2-6x^2y+9xy