Trigonometry (10th Edition)

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

Chapter 7 - Applications of Trigonometry and Vectors - Section 7.2 The Ambiguous Case of the Law of Sines - 7.2 Exercises - Page 304: 3

Answer

(a) If $4 \lt L \lt 5$, we can draw two triangles. (b) If $L = 4$ or $L \gt 5$, we can draw exactly one triangle. (c) If $L \lt 4$, the line is not long enough to meet the x-axis, so we can draw no triangle.

Work Step by Step

If the line has length $4$, we can draw a vertical line straight down to the x-axis. If $L \gt 4$, we could draw two lines from the point down to meet the x-axis. However, if $L \gt 5$, one of these two lines will meet the negative x-axis. (a) If $4 \lt L \lt 5$, we can draw two triangles. (b) If $L = 4$ or $L \gt 5$, we can draw exactly one triangle. (c) If $L \lt 4$, the line is not long enough to meet the x-axis, so we can draw no triangle.
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