Find the distance x in the diagram below (not to scale) - Leaving Cert Mathematics - Question 6 - 2017

To calculate the distance $y$, we can again apply the cosine rule:

$y^2 = a^2 + b^2 - 2ab \cdot \cos(C)$

Where:

• $a = 8.5$ cm
• $b = 10.2$ cm
• $C = 53.8^\circ$

Thus:

$y^2 = (8.5)^2 + (10.2)^2 - 2 \cdot (8.5) \cdot (10.2) \cdot \cos(53.8^\circ)$

Calculating each term:

1. $y^2 = 72.25 + 104.04 - 2 \cdot 8.5 \cdot 10.2 \cdot 0.5736$.
2. Then, plug in the values: $y^2 = 72.25 + 104.04 - 84.04 \approx 92.25$
3. Finally, take the square root: $y \approx \sqrt{92.25} \approx 9.61 \text{ cm}$

Therefore, the distance y is approximately 9.61 cm.