University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.3 - Trigonometric Functions - Exercises - Page 28: 60


The length of side $c$ is approximately $1.951$

Work Step by Step

$$a = 2 \hspace{1cm}b=3\hspace{1cm}C=40^\circ$$ - Recall the law of cosines: $$c^2=a^2+b^2-2ab\cos C$$ Therefore, we can calculate the length of side $c$: $$c^2=2^2+3^2-2\times2\times3\times\cos40^\circ$$ - Here there is no exact value of $\cos40^\circ$, so we would take an approximate value from calculator, which I would take $\cos40^\circ\approx0.766$ $$c^2=4+9-12\times0.766$$ $$c^2=13-9.192$$ $$c^2=3.808$$ $$c\approx1.951$$ (because the length of a side of a triangle is positive)
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