The diagram shows triangle ABC - OCR - GCSE Maths - Question 14 - 2020 - Paper 1

To find the length AB (denoted as c), we can use the Law of Cosines:

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

Where:

• a = AC = 15 cm
• b = BC = 18 cm
• C = angle BAC = 72°

Substituting the values:

$c^2 = 15^2 + 18^2 - 2 \cdot 15 \cdot 18 \cdot \cos(72°)$

Calculating further:

$c^2 = 225 + 324 - 540 \cdot \cos(72°)$ $c^2 = 549 - 540 \cdot 0.309 = 549 - 166.86$ $c^2 ≈ 382.14$

Taking the square root:

$c ≈ \sqrt{382.14} ≈ 19.55$

Thus, rounding to 3 significant figures, the length AB is:

AB ≈ 19.6 cm.