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: 18

Answer

$\angle B = 23.75^{\circ}$ $a \approx 4663$ yd $b \approx 1955$ yd

Work Step by Step

1. Find $\angle B$ $\angle A = 180 - (\angle A + \angle C)$ $= 180 - (106.1 + 50.15)$ $= 180 - 156.25$ $= 23.75^{\circ}$ 2. Find $a$ $\frac{a}{sin(A)} = \frac{c}{sin(C)}$ $\frac{a}{sin(106.1)} = \frac{3726}{sin(50.15)}$ $a = \frac{3726sin(106.1)}{sin(50.15)}$ by GDC / calculator $a = 4662.952...$ $a \approx 4663$ yd 3. Find $b$ $\frac{b}{sin(B)} = \frac{c}{sin(C)}$ $\frac{b}{sin(23.75)} = \frac{3726}{sin(50.15)}$ $b = \frac{3726sin(23.75)}{sin(50.15)}$ by GDC / calculator $b = 1954.6515...$ $b \approx 1955$ yd
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