Question

В треугольнике АВС <С = 90°, cos<B = 0,6 , ВС= 12 см, найти АВ​

Answer 1

Ответ:

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Объяснение:

Answer 2

Problem Statement

We are given a triangle ABC, where angle C is 90 degrees, cos angle B is 0.6, and BC is 12 cm. We need to find the length of AB.

Solution

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, we have a right triangle ABC, where angle C is 90 degrees. Let's label the sides as follows: - AB is the hypotenuse. - BC is the side adjacent to angle B. - AC is the side opposite angle B.

According to the Pythagorean theorem, we have the following equation: AB^2 = BC^2 + AC^2

Since we know the value of BC (12 cm), we need to find the value of AC to solve for AB.

To find AC, we can use the cosine function. The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. In this case, we know that cos angle B is 0.6, which means that BC/AB = 0.6.

We can rewrite this equation as: BC = AB * cos angle B

Substituting the known values, we have: 12 = AB * 0.6

Now we can solve for AB: AB = 12 / 0.6

Calculating this, we find: AB = 20 cm

Therefore, the length of AB is 20 cm.

Conclusion

In the given triangle ABC, with angle C equal to 90 degrees, cos angle B equal to 0.6, and BC equal to 12 cm, the length of AB is 20 cm.