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

To find the length AB in triangle ABC, we will use the Cosine Rule, which is given by:

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

Let:

• $c = AB$ (the side we want to find)
• $a = AC = 15 cm$
• $b = BC = 18 cm$
• $C = BAC = 72°$

Substituting the known values into the formula:

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

Calculating each component:

• $15^2 = 225$
• $18^2 = 324$
• $\cos(72°) \approx 0.3090$ (use a calculator)

Thus,

$AB^2 = 225 + 324 - 2 \cdot 15 \cdot 18 \cdot 0.3090$ $AB^2 = 225 + 324 - 2 \cdot 15 \cdot 18 \cdot 0.3090$ $AB^2 = 549 - 167.16$ $AB^2 = 381.84$

Finally, taking the square root:

$AB = \sqrt{381.84} \approx 19.54 cm$

Rounding to three significant figures, we get:

$AB \approx 19.5 cm$