Question

У трикутнику АВС відомо, що АВ=10 см, Вс= 6 см і кут В= 60 градусів. Знайти сторону АС

Answer 1

AC^2 = AB^2 + BC^2 - 2AB*AC*cosB
100 + 36 - 60 =76. Это AC^2, ну а AC будет корень из этого числа 

Answer 2

Finding the length of side AC in triangle ABC

To find the length of side AC in triangle ABC, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

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

In this case, we know that side AB is 10 cm, side BC is 6 cm, and angle B is 60 degrees. We want to find the length of side AC.

Let's substitute the given values into the Law of Cosines equation:

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

AC^2 = 10^2 + 6^2 - 2 * 10 * 6 * cos(60)

Simplifying further:

AC^2 = 100 + 36 - 120 * cos(60)

Using the value of cos(60) from a trigonometric table or calculator:

AC^2 = 100 + 36 - 120 * 0.5

AC^2 = 100 + 36 - 60

AC^2 = 76

Taking the square root of both sides:

AC = √76

Calculating the square root of 76, we get:

AC ≈ 8.72 cm

Therefore, the length of side AC in triangle ABC is approximately 8.72 cm.