Question

Дан прямоугольный треугольник АВС с прямым углом С, СА = 12 см, CВ = 16 см. Вычислите АВ и напишите тригонометрические соотношения угла В. При необходимости ответы округляйте до сотых. Ответ:

Answer 1

По-моему так по крайней мере вычисление стороны должно быть верно

Answer 2

Given Information:

We are given a right triangle ABC with a right angle at C. The lengths of CA and CB are given as CA = 12 cm and CB = 16 cm.

Finding AB:

To find the length of AB, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, AB is the hypotenuse, and CA and CB are the other two sides. Therefore, we have:

AB^2 = CA^2 + CB^2

Substituting the given values, we get:

AB^2 = 12^2 + 16^2

AB^2 = 144 + 256

AB^2 = 400

Taking the square root of both sides, we find:

AB = √400

AB = 20 cm

Therefore, the length of AB is 20 cm.

Trigonometric Ratios of Angle B:

To find the trigonometric ratios of angle B, we can use the lengths of the sides of the triangle.

The sine of angle B (sin B) is defined as the ratio of the length of the side opposite angle B (CB) to the length of the hypotenuse (AB):

sin B = CB / AB

Substituting the given values, we have:

sin B = 16 / 20

sin B = 0.8

The cosine of angle B (cos B) is defined as the ratio of the length of the side adjacent to angle B (CA) to the length of the hypotenuse (AB):

cos B = CA / AB

Substituting the given values, we have:

cos B = 12 / 20

cos B = 0.6

The tangent of angle B (tan B) is defined as the ratio of the length of the side opposite angle B (CB) to the length of the side adjacent to angle B (CA):

tan B = CB / CA

Substituting the given values, we have:

tan B = 16 / 12

tan B = 1.3333 (rounded to four decimal places)

Therefore, the trigonometric ratios of angle B are:

sin B = 0.8 cos B = 0.6 tan B = 1.3333 (rounded to four decimal places)

Note: The answers have been rounded to two decimal places, as specified in the question.