In the adjoining figure, $$AB = 9\text{ cm}$$, $$AC = 7\text{ cm}$$, $$BC = 8\text{ cm}$$, $$AD$$ is the median and $$\angle C = 40^\circ$$. Then the measure of $$\angle ADB$$ in degrees is
Solution
The three side lengths give $$\cos C = \frac{AC^2+BC^2-AB^2}{2\cdot AC\cdot BC} = \frac{2}{7}$$, so $$\angle C$$ is approximately $$73.4^\circ$$ and not $$40^\circ$$. Therefore no triangle satisfies all the stated conditions and none of the printed options is valid. The source treats this as a bonus problem, so the answer letter is only a required placeholder.
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