Question

В треугольнике АВС угол С равен 90градусов, ВС=4, синусВ равен 2корень из 6, дел на 5. Найти АВ

Answer 1

АВ = ВС * sinB = 4 * (2√6)/5=(8√6)/5
АС = АВ * sinВ = ((8√6)/5) * (2√6)/5 = 96/25

Answer 2

Given Information:

We are given the following information about triangle ABC: - Angle C is 90 degrees. - Length of side BC (denoted as CS) is 4. - The sine of angle B, sin(B), is equal to (2√6)/5.

Approach to Find AB:

To find the length of side AB (denoted as AS), we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 other two sides.

In our case, side AB is the hypotenuse, and sides BC and AC are the other two sides. By applying the Pythagorean theorem, we can find the length of AB.

Let's solve for AB:

Step 1: Recall the Pythagorean theorem: AB² = BC² + AC²

Step 2: Substitute the given values into the equation: AB² = 4² + AC²

Step 3: Simplify: AB² = 16 + AC²

Step 4: Recall that sin(B) = opposite/hypotenuse. In our case, sin(B) = AC/AB. Substitute the given value of sin(B): (2√6)/5 = AC/AB

Step 5: Rearrange the equation to solve for AC: AC = (2√6)/5 * AB

Step 6: Substitute the value of AC from step 5 into the equation from step 3: AB² = 16 + ((2√6)/5 * AB)²

Step 7: Simplify the equation: AB² = 16 + (4/25 * 6 * AB²)

Step 8: Multiply through by 25 to eliminate the fraction: 25 * AB² = 400 + 24 * AB²

Step 9: Simplify the equation: 25 * AB² - 24 * AB² = 400

Step 10: Combine like terms: AB² = 400

Step 11: Take the square root of both sides: AB = √400

Step 12: Simplify: AB = 20

Answer:

The length of side AB in triangle ABC is 20.