Question

В треугольнике АВс угол с 90. ВС 3, косА 2корень из 6 черта дроби 5.найти АВ

Answer 1

Сонечка я же посылала ответ на эту задачу что не пришло я сейчас поищу фото 

Answer 2

Triangle ABC with a Right Angle at C

To find the length of side AB in triangle ABC, we are given the following information:

- Angle BAC (angle A) is 90 degrees. - Side BC (side c) is 3. - The cosine of angle BAC (cos A) is 2√6/5.

We can use the Pythagorean theorem and trigonometric ratios to solve for the length of side AB.

Solution:

Let's denote side AB as a.

Using the Pythagorean theorem, we know that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, we have:

a^2 = BC^2 + AC^2

Since angle BAC is 90 degrees, we can use the trigonometric ratio cosine to find the length of side AC.

cos A = AC / BC

Substituting the given values:

2√6/5 = AC / 3

Simplifying, we find:

AC = (2√6/5) * 3 = 6√6/5

Now we can substitute the values of BC and AC into the Pythagorean theorem equation:

a^2 = 3^2 + (6√6/5)^2

Simplifying further:

a^2 = 9 + (36*6/25)

a^2 = 9 + 216/25

a^2 = (225 + 216) / 25

a^2 = 441 / 25

Taking the square root of both sides, we find:

a = √(441 / 25)

Simplifying:

a = 21 / 5

Therefore, the length of side AB is 21/5.

Conclusion:

In triangle ABC, with a right angle at C, if side BC is 3 and the cosine of angle BAC is 2√6/5, then the length of side AB is 21/5.