Trigonometry (10th Edition)

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

Chapter 2 - Acute Angles and Right Triangles - Section 2.5 Further Applications of Right Triangles - 2.5 Exercises: 20

Answer

The distance between the two lighthouses is $5856~m$

Work Step by Step

The angle in the triangle at lighthouse A is $180^{\circ}-129^{\circ}43'$ which is $50^{\circ}17'$ Let $d$ be the distance between the two lighthouses. Note that $d$ is the hypotenuse of the triangle. We can find $d$: $\frac{3742~m}{d} = cos~50^{\circ}17'$ $d = \frac{3742~m}{cos~50^{\circ}17'}$ $d = 5856~m$ The distance between the two lighthouses is $5856~m$
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