Question

Use the image to answer the question.

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.

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
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Answer 1

By the Law of Sines, b / sin(B) = c / sin(C). Here C = 180° − 14° − 52° = 114°, so

b = c * sin(B) / sin(C) = 17 * sin(52°) / sin(114°)
≈ 17 * 0.78801 / 0.91355 ≈ 14.67 cm.

Rounded to the nearest centimeter: 15 cm.