Triangle upper A upper B upper C has each of the interior angles by its vertices labeled with singular arcs. Side upper A upper B is labeled c, side upper A upper C is labeled b, and side upper B upper C is labeled a.

Question

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.

(1 point)
cm

Answer 1

To find the length of side b using the Law of Sines, we can use the formula:

sin A / a = sin B / b

Substitute the given values:

sin 14° / 17 = sin 52° / b

Now, solve for b:

b = 17 * sin 52° / sin 14°

b = 17 * 0.788 / 0.241

b ≈ 55.63 cm

Therefore, the length of side b is approximately 56 cm.