The diagram shows a circle, centre O - Edexcel - GCSE Maths - Question 23 - 2019 - Paper 3

Using the definition of tangent, we have:

$\tan(30^{\circ}) = \frac{p}{16 - 3p}$

Since ( \tan(30^{\circ}) = \frac{1}{\sqrt{3}} ), we can set up the equation as:

$\frac{p}{16 - 3p} = \frac{1}{\sqrt{3}}$.

Cross-multiplying gives us:

$p \sqrt{3} = 16 - 3p$

Bringing all terms involving p to one side results in:

$p \sqrt{3} + 3p = 16$

Factoring out p yields:

$p(\sqrt{3} + 3) = 16$

Thus, we can solve for p:

$p = \frac{16}{\sqrt{3} + 3}$.

Using a calculator, compute:

$p \approx \frac{16}{4.732} \approx 3.38$

Rounding to one decimal place gives:

$p \approx 3.4$.