The tangent of an acute angle of a right-angled triangle is the ratio of the length of the adjacent leg to the length of the opposite leg.
tgA = AC / BC.
AC = BC * tgA = 7 * √2 / 4 = (7 * √2) / 4.
By the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = BC ^ 2 + AC ^ 2 = 49 + 49 * 2/16 = (784 + 98) / 16 = 441/8.
AB = 21 / √8 = 21/2 * √2 = 5.25 * √2 cm.
Answer: Length AB = 5.25 * √2 cm.
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