In the triangle ABC, the angle is C 90 degrees, AB 104, AC 40. Find the tangent A.

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

If a triangle has an angle equal to 90º, then this triangle is right-angled. The side opposite the right angle is called the hypotenuse, and the other two are called legs.

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.

For this it is necessary to calculate the BC leg. Let’s 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;

BC ^ 2 = AB ^ 2 – AC ^ 2;

BC ^ 2 = 104 ^ 2 – 40 ^ 2 = 10816 – 1600 = 9216;

BC = √9216 = 96 cm.

tg A = 96/40 = 2.4.

Answer: the tangent of angle A is 2.4.