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: 19

Answer

$C = 82^{\circ}26'$ $b = 283.2~m$ $c = 415.2~m$

Work Step by Step

We can find angle $C$: $A+B+C = 180^{\circ}$ $C = 180^{\circ}- A -B$ $C = 180^{\circ}- 39^{\circ}54' -42^{\circ}32'$ $C = 82^{\circ}26'$ We can find the length of side $b$: $\frac{b}{sin~B} = \frac{a}{sin~A}$ $b = \frac{a~sin~B}{sin~A}$ $b = \frac{(268.7~m)~sin~(42^{\circ}32')}{sin~(39^{\circ}54')}$ $b = \frac{(268.7~m)~sin~(42.53^{\circ})}{sin~(39.9^{\circ})}$ $b = 283.2~m$ We can find the length of side $c$: $\frac{c}{sin~C} = \frac{a}{sin~A}$ $c = \frac{a~sin~C}{sin~A}$ $c = \frac{(268.7~m)~sin~(82^{\circ}26')}{sin~(39^{\circ}54')}$ $c = \frac{(268.7~m)~sin~(82.43^{\circ})}{sin~(39.9^{\circ})}$ $c = 415.2~m$
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