Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 7 - Section 7.2 - The Law of Cosines - 7.2 Problem Set: 13

Answer

The largest angle is $C = 67.4^{\circ}$.

Work Step by Step

1. Find $\angle B$ $cos(B) = \frac{a^{2} + c^{2} -b^{2}}{2ac}$ $cos(B) = \frac{(13)^{2} + (15)^{2} -(14)^{2}}{2(13)(15)}$ $cos(B) = \frac{198}{2(13)(15)}$ $cos(B) = \frac{198}{390}$ $cos(B) = 0.50769...$ by GDC / calculator $B = cos^{-1}(0.50796...)$ $B = 59.4897...^{\circ}$ $B = 59.5^{\circ}$ 2. Find $\angle A$ $cos(A) = \frac{b^{2} + c^{2} -a^{2}}{2bc}$ $cos(A) = \frac{(14)^{2} + (15)^{2} -(13)^{2}}{2(14)(15)}$ $cos(A) = \frac{252}{420}$ $cos(A) = 0.6$ by GDC / calculator $A = 53.1^{\circ}$ 3. Find $\angle C$ $cos(C) = \frac{a^{2} + b^{2} -c^{2}}{2ab}$ $cos(C) = \frac{(13)^{2} + (14)^{2} -(15)^{2}}{2(13)(14)}$ $cos(C) = \frac{140}{364}$ $cos(C) = 0.384615...$ by GDC / calculator $C = 67.38^{\circ}$ $C = 67.4^{\circ}$ $C \gt B \gt A$ Therefore the largest angle is $C = 67.4^{\circ}$.
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