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)
