In a right-angled triangle ABC (C = 90 degrees) AC = 5 cm, BC = 5 cm. Find the angle B and the hypotenuse AB

A rectangular triangle is a triangle in which one of the corners is a straight line, that is, it is equal to 90º.

To calculate the length of 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 = 5 ^ 2 + 5 ^ 2 = 25 + 25 = 50;

AB = √50 ≈ 7.1 cm.

We calculate the degree measure of the angle ∠B through the tangent of the angle. The tangent of an acute angle of a right triangle is the ratio of the opposite leg to the adjacent one:

tg B = AC / BC;

tg B = 5/5 = 1;

1 = tg 45º.

Answer: the length of the hypotenuse AB is 7.1 cm, the degree measure of the angle B is 45º.