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: 27

Answer

The ship traveled 17.8 km

Work Step by Step

Let $A = 44.2^{\circ}$ and let $B = 38.8^{\circ}$. Let the lighthouse be located at position of angle $C$. We can find angle $C$: $A+B+C = 180^{\circ}$ $C = 180^{\circ}-A-B$ $C = 180^{\circ}-44.2^{\circ}-38.8^{\circ}$ $C = 97.0^{\circ}$ Let $a = 12.5~km$. We can find the length of side $c$ which is the distance that the ship traveled: $\frac{c}{sin~C} = \frac{a}{sin~A}$ $c = \frac{a~sin~C}{sin~A}$ $c = \frac{(12.5~km)~sin~(97.0^{\circ})}{sin~(44.2^{\circ})}$ $c = 17.8~km$ The ship traveled 17.8 km
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