In triangle ABC, angle C is 90 degrees, tgA = 3/4, AC = 4. Find AB.

A triangle is three points that do not lie on one straight line, connected by segments. These points are called the vertices of the triangle, and the line segments are called its sides.

A triangle is called rectangular if one of its angles is straight (equal to 90º). The side opposite the right angle is called the hypotenuse, and the other two are called legs.

Since the tangent of angle A is known by the condition of the problem, in order to calculate the length of the hypotenuse AB, you need to calculate the length of the leg BC.

The tangent of an acute angle of a right triangle is the ratio of the opposite leg to the adjacent leg:

tg А = ВС / АС.

BC = AC · tg A;

BC = 4 * 3/4 ​​= 12/4 = 3 cm.

To calculate the hypotenuse AB, we use the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

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

AB ^ 2 = 4 ^ 2 + 3 ^ 2 = 16 + 9 = 25;

AB = √25 = 5 cm.

Answer: the length of the hypotenuse AB is 5 cm.