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: 15

Answer

$\angle B \approx 110.0^{\circ}$ $a \approx 27.01$ m $c \approx 21.36$ m

Work Step by Step

1. Find $\angle B$ $\angle B = 180 - (30.35 + 39.7)$ $= 180 - (70.05)$ $= 109.95^{\circ}$ $\approx 110.0^{\circ}$ 2. Find $a$ $\frac{a}{sin(A)} = \frac{39.74}{sin(B)}$ $\frac{a}{sin(39.7)} = \frac{39.74}{sin(109.95)}$ $a = \frac{39.74sin(39.7)}{sin(109.95)}$ by GDC / calculator $a = 27.005$ m $a \approx 27.01$ m 3. Find $c$ $\frac{c}{sin(C)} = \frac{b}{sin(B)}$ $\frac{c}{sin(30.35)} = \frac{39.74}{sin(109.95)}$ $c = \frac{39.74sin(30.35)}{sin(109.95)}$ by GDC / calculator $c = 21.3617...$ m $c \approx 21.36$ m
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