In the triangle, angle B is 52 degrees and angle A is 14 degrees. If side c has a length of 17 cm, use the Law of Sines to find the length of side b. Round your answer to the nearest centimeter.
To find the length of side b, we can use the Law of Sines formula:
a/sin(A) = c/sin(C)
First, we need to find angle C:
C = 180 - A - B
C = 180 - 14 - 52
C = 114 degrees
Now, we can plug in the values and solve for side b:
b/sin(B) = c/sin(C)
b/sin(52) = 17/sin(114)
b = (17 * sin(52)) / sin(114)
b = (17 * 0.7880) / 0.9271
b = 13.414
Therefore, the length of side b is approximately 13 cm.