Question

В ΔABC, ∠A=30*, ∠B=45*, BC=10√2 Найти: AC - ?

Answer 1

теорема синусов
a/sinA=b/sinB
$x = (10 \sqrt{2} \times \frac{ \sqrt{2} }{2}) \div \frac{1}{2} = 10 \times 2 = 20 =$

Answer 2

To find AC, we can use the Law of Cosines, which relates the side lengths of a triangle to the cosine of one of its angles. The Law of Cosines is given by:

c^2 = a^2 + b^2 - 2ab * cos(C)

Where: c = length of the side opposite angle C (in this case, BC = 10√2) a = length of one side adjacent to angle C (in this case, AC) b = length of the other side adjacent to angle C (in this case, AB)

Let's find AB first. Since we know the measure of angle B (45 degrees) and the length of BC (10√2), we can use trigonometric ratios to find AB.

sin(B) = opposite / hypotenuse sin(45 degrees) = AB / 10√2 AB = 10√2 * sin(45 degrees) = 10√2 * (1/√2) = 10.

Now we have AB = 10.

Now, we can use the Law of Cosines again to find AC:

AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(A)

Since cos(30 degrees) = √3/2:

AC^2 = 10^2 + (10√2)^2 - 2 * 10 * 10√2 * (√3/2) AC^2 = 100 + 200 - 100√3 AC^2 = 300 - 100√3

To find AC, take the square root of both sides:

AC = √(300 - 100√3)

Now, let's calculate the approximate value of AC:

AC ≈ √(300 - 100 * 1.732) ≈ √(300 - 173.2) ≈ √126.8 ≈ 11.26

So, AC ≈ 11.26.