Since triangle ABC is inscribed in a circle with AB as the diameter, angle C is a right angle according to the inscribed angle theorem. This means that angle B is not directly calculated but can be found using the sides of the triangle.
Given:
- AB = 14 cm
- AC = 8 cm
Using the Pythagorean theorem, we can find the length of side BC. Let the length of BC be represented as \( c \).
According to the Pythagorean theorem:
\[ AC^2 + BC^2 = AB^2 \]
Substituting the values we have:
\[ 8^2 + c^2 = 14^2 \]
This simplifies to:
\[ 64 + c^2 = 196 \]
Subtracting 64 from both sides gives:
\[ c^2 = 196 - 64 \] \[ c^2 = 132 \] \[ c = \sqrt{132} \approx 11.49 \text{ cm} \]
Now, we can use the sine rule or tangent to find angle B.
Using the sine function:
\[ \sin(B) = \frac{AC}{AB} \]
Substituting the known lengths:
\[ \sin(B) = \frac{8}{14} = \frac{4}{7} \approx 0.5714 \]
Now, we calculate angle B:
\[ B \approx \arcsin(0.5714) \approx 35° \]
Thus, the approximate angle measure of B is 35°.