Trigonometry 7th Edition

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

Chapter 2 - Section 2.3 - Solving Right Triangles - 2.3 Problem Set - Page 81: 58

Answer

Chapter 2 - Section 2.3 Problem Set: 58 (Answer) Refer to Figure 1 $\angle CAE$ = 4.6$^{\circ}$ (To the nearest tenths)

Work Step by Step

Chapter 2 - Section 2.3 Problem Set: 58 (Solution) Refer to Figure 1 In $\triangle$CAB, $\tan \angle CAB$ = $\frac{CB}{AB}$ $\tan \angle CAB$ = $\frac{(12+54)}{54}$ $\angle CAB$ = $\tan^{-1}(\frac{66}{54})$ $\angle CAB$ = 50.7$^{\circ}$ (To the nearest tenths) In $\triangle$EAB, $\tan \angle EAB$ = $\frac{EB}{AB}$ $\tan \angle EAB$ = $\frac{(24+54)}{54}$ $\angle EAB$ = $\tan^{-1}(\frac{78}{54})$ $\angle EAB$ = 55.3$^{\circ}$ (To the nearest tenths) $\angle CAE$ = $\angle EAB$ - $\angle CAB$ $\angle CAE$ = 55.3$^{\circ}$ - 50.7$^{\circ}$ $\angle CAE$ = 4.6$^{\circ}$ (To the nearest tenths)
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