Answer
$\sin$ 28$^{\circ}$ 14' $\cos$ 61$^{\circ}$ 46' + $\cos$ 28$^{\circ}$ 14' sin 61$^{\circ}$ 46' $\approx$ 1
Work Step by Step
$\sin$ 28$^{\circ}$ 14' $\cos$ 61$^{\circ}$ 46' + $\cos$ 28$^{\circ}$ 14' sin 61$^{\circ}$ 46'
Convert minutes to decimals:
$\frac{14}{60}$ = 0.2333
$\frac{46}{60}$ = 0.7666
Therefore:
$\sin$ 28$^{\circ}$ 14' $\cos$ 61$^{\circ}$ 46' + $\cos$ 28$^{\circ}$ 14' sin 61$^{\circ}$ 46'
= $\sin$ 28.2333$^{\circ}$ $\cos$ 61.7666$^{\circ}$ + $\cos$ 28.2333$^{\circ}$ sin 61.7666$^{\circ}$
$\sin$ 28.2333$^{\circ}$ $\cos$ 61.7666$^{\circ}$ + $\cos$ 28.2333$^{\circ}$ sin 61.7666$^{\circ}$
$\approx$(0.4731)(0.4731) + (0.8810)(0.8810)
$\approx$ 0.2238 + 0.7761
$\approx$ 0.9999
$\approx$ 1
Therefore:
$\sin$ 28$^{\circ}$ 14' $\cos$ 61$^{\circ}$ 46' + $\cos$ 28$^{\circ}$ 14' sin 61$^{\circ}$ 46' $\approx$ 1
