# The two sides of the triangle, the lengths of which are 3: 8, form an angle of 60 degrees.

August 30, 2021 | education

| **The two sides of the triangle, the lengths of which are 3: 8, form an angle of 60 degrees. Find these sides if the third side is 21 cm.**

Let us denote the length of one part of the side of the triangle by variable x. Then the lengths of the sides of the triangle are 3x and 8x, respectively.

According to the cosine theorem:

a ^ 2 = b ^ 2 + c ^ 2 – 2bc * cosα, where a is the length of the side opposite to the angle α (a = 21 cm), b is the length of the second side of the triangle (b = 3x), c is the length of the third side of the triangle (c = 8x), α = 60º.

21 ^ 2 = (3x) ^ 2 + (8x) ^ 2 – 2 * 3x * 8x * cos60º.

441 = 9x ^ 2 + 64x ^ 2 – 24x ^ 2.

441 = 49x ^ 2.

x ^ 2 = 441/49.

x = √9 = 3.

b = 3x = 3 * 3 = 9 cm.

c = 8x = 8 * 3 = 24 cm.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.