Edexcel C2 sine and cosine rule help

I don't understand how to work out Exercise 2F question 6c). Any help on how to find x? See attachment for question. Thanks :smile:

It's quite difficult. Can you find any of the other lengths or angles? This will allow you to work towards the one you want.

I don't understand how to work out Exercise 2F question 6c). Any help on how to find x? See attachment for question. Thanks :smile:

The angle ACB is 130.
Let BC be y then with cosine rule

11^2=3.8^2+y^2-7.6\cdot y\cdot \cos 130^o

from this you will get y

Let the BAC angle is

\alpha

WIth cosine rule

y^2=3.8^2+11^2-7.6\cdot 11\cdot \cos \alpha

from this you will get

\alpha

Then a sine rule for triangle ADC will give the angle x
the angle ADC is

180^o-\alpha - x

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