# In a triangle abc, the angle C is 90 * AB = 6, tgA = √3. Find the AC.

December 29, 2020 | education

| First way.

Since tgBAC = √3, the angle BAC = arctan√3 = 600.

The sum of the acute angles of a right-angled triangle is 600, then the angle ABC = 90 – 60 = 300.

The AC leg lies against an angle of 300, then AC = AB / 2 = 6/2 = 3 cm.

Second way.

tgBAC = √3 = BC / AC, then let BC = X cm, AC = X * √3 cm.

By the Pythagorean theorem, AB ^ 2 = BC ^ 2 + AC ^ 2.

36 = X ^ 2 + 3 * X ^ 2.

4 * X ^ 2 = 36.

X ^ 2 = 9.

X = BC = 3 cm.

Answer: The length of the BC leg is 3 cm.

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