The diagram shows a right-angled triangle - OCR - GCSE Maths - Question 22 - 2023 - Paper 2

To find the length of side 'a' in the right-angled triangle, we can use trigonometric ratios. Since we have the angle (30°) and the side opposite to it (14 cm), we can use the sine function:

1. The formula for sine in a right triangle is:

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

2. Here, we know:

   • Opposite side = 14 cm
   • Angle ( \theta = 30° )

3. Therefore, according to the sine function:

   $\sin(30°) = \frac{14}{a}$

4. We know that ( \sin(30°) = \frac{1}{2} ). Substituting this into the equation:

   $\frac{1}{2} = \frac{14}{a}$

5. To solve for 'a', we cross-multiply:

   $1 \cdot a = 2 \cdot 14$

6. Thus, we find:

   $a = 28 \text{ cm}$

So, the value of 'a' is:

a = 28 cm