Based on the given information, the length of side AC in triangle ABC is approximately 22.641 cm.
How to calculate the required length
In a triangle, the circumradius (R) is related to the side lengths by the formula:
R = (abc) / (4A)
Where a, b, and c are the side lengths of the triangle, and A is the area of the triangle.
In triangle ABC, the given angle B is 49°.
Use the Law of Sines to find the length of side AC.
According to law of Sines:
sin(A) / a = sin(B) / b
Given that B is 49°, set up the equation as follows:
sin(A) / AC = sin(49°) / BC
Since the circumradius (R) is given as 15 cm
AC = 2R * sin(A)
Substitute this into the equation above
sin(A) / (2R * sin(A)) = sin(49°) / BC
1 / (2R) = sin(49°) / BC
Now, substitute the value of R (15 cm) and solve for BC:
1 / (2 * 15) = sin(49°) / BC
BC = sin(49°) * (2 * 15)
Using a calculator to evaluate sin(49°) ≈ 0.7547
BC ≈ 0.7547 * (2 * 15)
BC ≈ 0.7547 * 30
BC ≈ 22.641 cm
Therefore, the length of side AC in triangle ABC is approximately 22.641 cm.