Sides of the triangle 5,7 and 8 find the angle opposite the middle side.

In the wording of the condition for this task, it is reported that the lengths of the sides of this triangle are 5, 7, and 8.

Therefore, the length of the middle side of the triangle is 7.

Let us denote the value of the angle opposite this side by x.

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

5 ^ 2 + 8 ^ 2 – 2 * 5 * 8 * cosx = 7 ^ 2,

solving which, we get:

25 + 64 – 80 * cosx = 49;

89 – 80 * cosx = 49;

80 * cosx = 89 – 49;

80 * cosx = 40;

cosx = 40/80 = 1/2;

x = arccos (1/2) = 60 °.

Answer: 60 °.