Sine Rule (Higher Tier)

Someone has asked for information on the Sine Rule. This is a Higher Tier topic.

Sine Rule is one of the harder topics in your GCSE, but if you learn how to use it correctly, there are easy marks to be gained. This is because you don't need to remember the formula for the Sine Rule as it is on your formula sheet (in your Edexcel exam)!

Go to the inside cover of your exam and you will see the following:

In any triangle ABC

Sine Rule:    a    =    b    =    c  
                 sinA     sinB      sinC




It can also be written as...

sinA  =  sinB  =  sinC
  a           b           c

Question

In this triangle, find the size of the angle marked x.



To find the angle marked x, we can use the Sine Rule.

From the information above, we know that this relationship is true:

sin x   =   sin 30      (A=x, a=12, B=30, b=10 - see first triangle above)
  12            10

Solution

sin x = 12sin 30  = 0.6
                10 
x = sin^(-1)(0.6)         (inverse sine of 0.6)
x = 36.9∘ (1 decimal place)

Remember: If we have "sin x = 0.6", to get x on its own we must calculate "inverse sine of 0.6". This can be done on your calculator (normally by pressing "shift, sine" to get inverse sine).

Top Tip: When answering Sine Rule questions, write down the Sine Rule first, then substitute (put in) the values from your triangle. If you do this, you will have shown some working which will hopefully get you some marks even if your final answer is wrong.

What's Next?
Similar questions will involve having to use the Cosine Rule, or to work out the area of a triangle using sine. Both of these formulae are also on the formula sheet page of your exam. Watch out for revision posts on these topics.