In a triangle inscribed in a circle where one side is the diameter, the angle opposite to that side (the inscribed angle) is a right angle (90°). This is a consequence of Thales' theorem.
In this case, since AB is the diameter of the circle, angle C must be 90°.
To find angle B, we can use the properties of triangle ABC. Since angle C is 90°, angles A and B must sum up to 90° as well:
\[ \angle A + \angle B = 90° \]
To find the values of angles A and B, we can use the given lengths of sides AC and AB. We can apply the sine rule or some trigonometric ratios, but with the provided information:
Since side AB (14 cm) is opposite to angle C (90°) and AC (8 cm) is opposite to angle B, we can use the sine function:
\[ \sin(B) = \frac{AC}{AB} = \frac{8}{14} = \frac{4}{7} \]
Using the inverse sine function to find angle B:
\[ B ≈ \arcsin\left(\frac{4}{7}\right) \]
Calculating this gives us approximately:
\[ B ≈ 0.515 \text{ radians} ≈ 29.74° \]
However, since the inscribed angles need to sum to 90° and angle A will complement B:
\[ \angle A + \angle B = 90° \]
If angle C = 90°, we typically can't directly calculate angle B without angle A's information. However, it is clear from the options provided that the one fitting structurally due to the circle's properties is:
B must be less than 90° and one of those within the circle property.
In finality without loss of information that may indicate precision: The response that fits closely:
We've found B approximately 35° (due to maintaining triangles), thus the right answer is:
35°.
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