The tangent of the angle is the ratio of the opposite leg to the adjacent one, then:
AC / BC = tgABC = √5 / 2 = AC / 10.
AC = (√5 / 2) * 10 = 5 * √5 cm.
From the right-angled triangle ABC, by the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = BC ^ 2 + AC ^ 2 = 10 ^ 2 + (5 * √5) ^ 2 = 100 + 125 = 225.
AB = √225 = 15 cm.
Answer: The length of side AB is 15 cm.
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