ABC is a right-angled triangle - Edexcel - GCSE Maths - Question 7 - 2017 - Paper 3

In triangle ABC, we can use the sine function since we know angle C and the length of side AC.

The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, we can write:

$\sin(23^\circ) = \frac{AB}{15}$

To find AB, we can rearrange the equation:

$AB = 15 \cdot \sin(23^\circ)$

Calculating this:

$AB \approx 15 \cdot 0.3907 \approx 5.86$

Rounding to 3 significant figures gives:

$AB \approx 5.86 \text{ cm}$