Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 7 - Applications of Trigonometry and Vectors - Section 7.1 Oblique Triangles and the Law of Sines - 7.1 Exercises: 16

Answer

$\angle A = 65.6^{\circ}$ $c \approx 2.727$ cm $b \approx 1.942$ cm

Work Step by Step

1. Find $\angle A$ $\angle A = 180 - (\angle B + \angle C)$ $= 180 - (42.57+71.83)$ $= 180 - 114.4$ $= 65.6^{\circ}$ 2. Find $b$ $\frac{b}{sin(B)} = \frac{a}{sin(A)}$ $\frac{b}{sin(42.57)} = \frac{2.614}{sin(65.6)}$ $b = \frac{2.614sin(42.57)}{sin(65.6)}$ by GDC / calculator $b = 1.94177...$ $b \approx 1.942$ cm 3. Find $c$ $\frac{c}{sin(C)} = \frac{a}{sin(A)}$ $\frac{c}{sin(71.83)} = \frac{2.614}{sin(65.6)}$ $c = \frac{2.614sin(71.83)}{sin(65.6)}$ by GDC / calculator $c = 2.72724...$ $c \approx 2.727$ cm
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