Final answer:
The length of side AB is calculated using the cosine of angle ACB, which results in AB being approximately 6.70 cm when rounded to three significant figures.
Step-by-step explanation:
The length of AB in the right triangle ABC can be calculated using trigonometry. Since we know the length of BC (8.5 cm) and the angle ACB (38°), we can use the cosine function. The formula is:
AB = BC × cos(ACB)
Plugging in the values we have, it becomes:
AB = 8.5 cm × cos(38°)
Using a calculator, we find that cos(38°) ≈ 0.7880, so the calculation is:
AB ≈ 8.5 cm × 0.7880
AB ≈ 6.698 cm
When rounded to three significant figures, the length of AB is approximately 6.70 cm.