Find the value of x.
Round to the nearest tenth.
х
3
120°
10
x = [?]
Law of Cosines: c2 = a2 + b2 - 2ab cos C
Enter

x = 11.8

Step-by-step explanation:

x² = 3² + 10² - 2(3)(10) · cos120°

x² = 109 - (60 · cos120°)

x² = 109 - (-30)

x² = 139

x = ≈ 11.8

look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3