In triangle ABC, angle c is 90, ac = 3, tgA = √7 divided by 3. Find AB

The tangent of angle A is the ratio of the opposite leg BC to the adjacent leg AC.

According to the condition, the tangent of the angle A is equal to √7: 3, the length of the leg AC = 3 cm.

Let’s find the length of the BC leg:

Tg A = BC: AC;

BC = AC × tan A;

BC = 3 × √7: 3;

BC = √7 cm.

Let’s find AB – the hypotenuse of a triangle according to the Pythagorean theorem:

AB ^ 2 = AC ^ 2 + BC ^ 2;

AB ^ 2 = 3 ^ 2 + (√7) ^ 2;

AB ^ 2 = 9 + 7;

AB ^ 2 = 16;

AB = √16;

AB = 4 cm.