Question

СРОЧНО!!!!!В ТРЕУГОЛЬНИКЕ АВС СТОРОНА АВ НА 4СМ БОЛЬШЕ ВС ,УГОЛ В =120°,АС=14 СМ.Найти АВ и ВС.

Answer 1

Теорема косинусов: квадрат стороны треугольника равен сумме квадратов двух других сторон минус удвоенное произведение этих сторон на косинус угла между ними:
AC²=AB²+BC²-2*AB*BC*cos∠B
Известно, что АВ=ВС+4. Подставляем все известные значения в формулу:
14²=(ВС+4)²+ВС²-2(ВС+4)*ВС*cos120°
196=BC²+8BC+16+BC²-2(BC+4)*BC*(-1/2)
196=2BC²+8BC+16+BC²+4BC
3BC²+12BC-196+16=0
3BC²+12BC-180=0 |:3
BC²+4BC-60=0
D=4²-4*(-60)=16+240=256=16²
BC=(-4-16)/2=-10 - не подходит
BC=(-4+16)/2=6 см
АВ=6+4=10 см

Ответ: АВ=10 см, ВС=6 см.

Answer 2

Finding the Lengths of AB and BC in Triangle ABC

To find the lengths of AB and BC in triangle ABC, we can use the given information about the triangle's side and angle measurements.

Given: - Side AB is 4 cm longer than side BC. - Angle A = 120°. - Side AC = 14 cm.

Calculating the Lengths of AB and BC

To calculate the lengths of AB and BC, we can use trigonometric relationships and the given information about the triangle.

First, we can use the law of sines to find the length of side AB. The law of sines states that in any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

Where a, b, and c are the side lengths, and A, B, and C are the opposite angles.

Using the law of sines, we can calculate the length of side AB:

AB/sin(120°) = 14/sin(B)

Next, we can use the fact that side AB is 4 cm longer than side BC:

AB = BC + 4

By substituting the value of AB from the law of sines equation, we can solve for BC.

Conclusion

By using the law of sines and the given information about the triangle, we can calculate the lengths of sides AB and BC in triangle ABC.