Треугольнике ABC угол а 45° угол b - 60°, б с = 3√2 найдите AC.

To solve this problem, we can use the law of sines. The law of sines states that in any triangle, the ratio of the length of a side to the sine of the opposite angle is constant.

In triangle ABC, we have angle A as 45°, angle B as 60°, and side BC as 3√2. Let's find side AC.

We can set up the following proportion using the law of sines:

BC/sin(A) = AC/sin(B)

Plugging in the values we know:

3√2 / sin(45°) = AC / sin(60°)

Since sin(45°) = sin(60°) = √3/2, we can simplify the equation to:

(3√2) / (√3/2) = AC / (√3/2)

Now, let's simplify the equation further:

(3√2) * (2/√3) = AC

6√2 / √3 = AC

To rationalize the denominator, we multiply the numerator and denominator by √3:

(6√2 * √3) / √3 * √3 = AC

(6√6) / 3 = AC

2√6 = AC

Therefore, the length of side AC is 2√6.