# In the triangle ABC, the angle is C = 90, tgA = √2 / 4, BC = 7. find AB

October 9, 2021 | education

| 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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