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: 17

Answer

$\angle A= 34.72^{\circ}$ $a \approx 3325$ ft $c \approx 5701$ ft

Work Step by Step

1. Find $\angle A$ $\angle A = 180 - (\angle B + \angle C)$ $= 180 - (42.88 + 102.40)$ $= 180 - 145.28$ $= 34.72^{\circ}$ 2. Find $a$ $\frac{a}{sin(A)} = \frac{b}{sin(B)}$ $\frac{a}{sin(34.72)} = \frac{3972}{sin(42.88)}$ $a = \frac{3972sin(34.72)}{sin(42.88)}$ by GDC / calculator $a = 3324.664...$ ft $a \approx 3325$ ft 3. Find $c$ $\frac{c}{sin(C)} = \frac{b}{sin(B)}$ $\frac{c}{sin(102.4)} = \frac{3972}{sin(42.88)}$ $c = \frac{3972sin(102.4)}{sin(42.88)}$ by GDC / calculator $c = 5701.0156...$ $c \approx 5701$ ft
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