Here is triangle ABC - Edexcel - GCSE Maths - Question 16 - 2021 - Paper 2

To find the length of side BC, we can use the Law of Cosines, which states:
$c^2 = a^2 + b^2 - 2ab \cdot \cos(C)$
where:

• $c$ is the side opposite angle C (in this case, BC),
• $a$ and $b$ are the other two sides (8 cm and 11 cm respectively),
• $C$ is the angle opposite side $c$ (72°).

Substituting the values:
$BC^2 = 8^2 + 11^2 - 2 \cdot 8 \cdot 11 \cdot \cos(72°)$
Calculating this gives:

1. $8^2 = 64$
2. $11^2 = 121$
3. The cosine of 72° is approximately $0.309$.

Thus:
$BC^2 = 64 + 121 - 2 \cdot 8 \cdot 11 \cdot 0.309$
$BC^2 = 185 - 2 \cdot 88 \cdot 0.309$
$BC^2 ≈ 185 - 54.528$
$BC^2 ≈ 130.472$
Taking the square root gives:
$BC ≈ \sqrt{130.472} ≈ 11.4 \, \text{cm}$
The length of BC is therefore approximately 11.4 cm, correct to 3 significant figures.