The diagram shows triangle ABC - Edexcel - GCSE Maths - Question 19 - 2019 - Paper 3

From the relationship we established:

$\angle DAC = \frac{2}{5} \angle BCA$

Therefore, once we find ( x ), we can compute ( \angle DAC ). Let’s find the values.

For triangle ADC, we can again apply the sine rule:

$\frac{AC}{\sin(\angle DAC)} = \frac{DC}{\sin(\angle ACD)}$

Where ( DC ) is what we are trying to find, and ( \angle ACD = 180 - (\angle DAC + \angle ABC) $$. We can substitute the known values to find ( DC ).

After substituting the values through sine rule, we arrive at:

$DC = \frac{6.2 \cdot \sin(\angle ACD)}{\sin(\angle DAC)}$

Substituting the values gives us the result. Make sure to round to three significant figures.