ABC is a right-angled triangle - Edexcel - GCSE Maths - Question 6 - 2019 - Paper 2

To find the length of side AB, we can use the sine function since we have an angle and the length of the opposite side (AC).

Using the sine formula:

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

In this case, we have:

$\sin(38^\circ) = \frac{AC}{AB}$

Substituting the known values:

$\sin(38^\circ) = \frac{16}{AB}$

To find AB, rearranging yields:

$AB = \frac{16}{\sin(38^\circ)}$

Calculating this gives approximately:

$AB \approx \frac{16}{0.6157} \approx 25.94 \text{ cm}$

Thus, the length of AB is approximately 25.94 cm.