Question

Помогите пожалуйста решить . Дан треугольник АВС. АВ = 7 см. ВС = 5 см. Угол ВСА = 60 градусов. Найти АС Применить теорему косинусов.

Answer 1

AB^2=AC^2+BC^2-2*AC*BC*cos(60)
49=AC^2+25-2*5*0.5*AC
AC^2-5*AC-24=0
D=25+96=121
AC1=-3
AC2=8
AC1 не удовлетворяет 
Ответ: 8

Answer 2

$AB ^{2}=BC ^{2}+AC ^{2}-2*BC*AC*cosC;$
$49=25+AC^{2}-2*5* \frac{1}{2}*AC=AC ^{2}-5AC+25;$
$AC^{2}-5AC-24=0;D=121; AC=8;AC=-3$ - постор корень
Ответ АС=8

Answer 3

Problem Statement

We are given triangle ABC, where AB = 7 cm, BC = 5 cm, and angle BCA = 60 degrees. We need to find the length of AC using the cosine theorem.

Solution

The cosine theorem 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 our case, we have AB = 7 cm, BC = 5 cm, and angle BCA = 60 degrees. We need to find AC.

Using the cosine theorem, we can substitute the given values into the equation:

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

AC^2 = 7^2 + 5^2 - 2 * 7 * 5 * cos(60)

AC^2 = 49 + 25 - 70 * cos(60)

AC^2 = 74 - 70 * 0.5

AC^2 = 74 - 35

AC^2 = 39

Taking the square root of both sides, we get:

AC = sqrt(39)

Therefore, the length of AC is approximately 6.24 cm.

Conclusion

Using the cosine theorem, we found that the length of AC in triangle ABC is approximately 6.24 cm.