One side of the triangle is 7cm, and the other two sides are 3: 8 and form an angle of 60 °.

One side of the triangle is 7cm, and the other two sides are 3: 8 and form an angle of 60 °. Find the perimeter of the triangle.

We denote by x one third of the length of that of the two unknown sides of the given triangle, which is the smaller.

Then this smaller side should be equal to 3x cm, and since the ratio of these two sides is 3: 8, the length of the second side should be equal to 8x cm.

Using the cosine theorem, we can write the following equation:

(3x) ^ 2 + (8x) ^ 2 – 2 * 3x * 8x * cos (60 °) = 7 ^ 2,

solving which, we get:

9x ^ 2 + 64x ^ 2 – 48x ^ 2 * 0.5 = 49;

73x ^ 2 – 24x ^ 2 = 49;

49x ^ 2 = 49;

x ^ 2 = 49/49;

x ^ 2 = 1;

x = 1.

Knowing x, we find the perimeter of the triangle:

3x + 8x + 7 = 11x + 7 = 11 * 1 + 7 = 18 cm.

Answer: 18 cm.