Yes, it is possible to use the law of cosines to solve for one angle in a triangle.
The law of cosines states that in any triangle, the square of the length of any side (c) is equal to the sum of the squares of the lengths of the other two sides (a and b) minus twice the product of those sides and the cosine of the angle between them (C):
c^2 = a^2 + b^2 - 2ab * cos(C)
If you know the lengths of all three sides of a triangle (a, b, and c), you can use the law of cosines to solve for the cosine of one of the angles (C). Once you have the cosine of the angle, you can use the inverse cosine function (also known as the arccosine) to find the measure of the angle in degrees.
For example, if you know the lengths of sides a and b and the measure of angle C in a triangle, you can use the law of cosines to find the length of side c:
c = sqrt(a^2 + b^2 - 2ab * cos(C))
Alternatively, if you know the lengths of sides a and c and the measure of angle B in a triangle, you can use the law of cosines to find the length of side b:
b = sqrt(c^2 - a^2 - 2ac * cos(B))
In both cases, once you have found the value of one of the sides, you can use the law of sines to find the measure of the remaining angle in the triangle.