In triangle ABC, angle C is 90 degrees, AC = 6, tg A = 3/4. Find AB.

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

A rectangular triangle is a triangle in which one corner is a straight line (equal to 90º). The side opposite to the right angle is called the hypotenuse, and the other two are called the legs.

In order to calculate the length of the hypotenuse AB, you need to calculate the length of the BC leg.

To do this, we will use the tangent of the angle. Tangent is the ratio of the opposite leg to the adjacent one:

tg A = BC / AC;

ВС = АС ∙ tg A;

BC = 6 * 3/4 ​​= 18/4 = 4.5 cm.

To calculate 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 = 4.5 ^ 2 + 6 ^ 2 = 20.25 + 36 = 56.25;

AB = √56.25 = 7.5 cm.

Answer: the length of the hypotenuse AB is 7.5 cm.
