Question

СРОЧНООО ПОМОГИТЕ ПЖ!!! МАТИМАТИКА 9-10 КЛАССДан ΔАВСАВ=3см, АС=4см,∡ВАС=60°. Найти сторону ВС.(темы...теорема синуса и косинуса)

Answer 1

против угла А сторона а ит.д.    по теор. косинусов а^2=b^2+c^2-2bc*cosA=16+9-2*4*3*cos 60=25-24*1/2=25-12=13

Answer 2

Problem Statement

We are given a triangle ABC, where ΔABC = 3 cm, AC = 4 cm, and ∡BAC = 60°. We need to find the length of side BC.

Solution

To find the length of side BC, we can use the Law of Cosines. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the two sides and the cosine of the included angle.

In this case, we can use the Law of Cosines to find the length of side BC. Let's denote BC as a, AB as b, and AC as c. According to the Law of Cosines, we have:

a^2 = b^2 + c^2 - 2bc * cos(∡BAC)

Substituting the given values, we have:

a^2 = 3^2 + 4^2 - 2 * 3 * 4 * cos(60°)

Simplifying the equation, we get:

a^2 = 9 + 16 - 24 * cos(60°)

Using the value of cos(60°) = 1/2, we have:

a^2 = 9 + 16 - 24 * (1/2)

a^2 = 9 + 16 - 12

a^2 = 13

Taking the square root of both sides, we get:

a = √13

Therefore, the length of side BC is √13 cm.

Conclusion

In conclusion, using the Law of Cosines, we have found that the length of side BC in triangle ABC is √13 cm.