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.

Answer 1

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.