Question

20. Знайдіть сторону AC трикутника АВС, якщо AB = 7 см, ВС = 13 см, ZA = 120°. ​

Answer 1

Ответ:

AC=8 см

Объяснение:

згідно теоремі синусів ВС/sin∠А=AB /sin∠С ⇒ 13*2/√3=7/sin∠С

sin∠С  =7/26*√3=0,466    ∠С  =27,8°

∠В  =180°-∠А-∠С=180-120-27,8°=32,2°

AC= 26/√3*sin32,2°=8 см

Answer 2

Finding the Side AC of Triangle ABC

To find the side AC of triangle ABC, given AB = 7 cm, BC = 13 cm, and ∠A = 120°, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and angle C opposite side c, the following equation holds true:

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

Using this formula, we can calculate the length of side AC.

Calculation

Substituting the given values: - a = AB = 7 cm - b = BC = 13 cm - C = ∠A = 120°

We can calculate the length of side AC using the law of cosines:

AC^2 = 7^2 + 13^2 - 2 * 7 * 13 * cos(120°)

Calculating the value of cos(120°): - cos(120°) = -0.5

Substituting the value of cos(120°) into the equation: AC^2 = 49 + 169 - 2 * 7 * 13 * (-0.5)

AC^2 = 49 + 169 + 91

AC^2 = 309

Taking the square root of both sides: AC ≈ √309

Result

AC ≈ 17.58 cm

So, the length of side AC of triangle ABC is approximately 17.58 cm.