#### Answer

$31^{\circ}$F

#### Work Step by Step

Since March $15$ corresponds to Day $74$, we substitute $x=74$ in the formula:
$T(74)=37+21\sin[\frac{2\pi}{365}(x-91)]$
$T(74)=37+21\sin[\frac{2\pi}{365}(74-91)]$
$T(74)=37+21\sin[\frac{2\pi}{365}(-17)]$
$T(74)=37+21\sin[-0.293]$
$T(74)=37+21(-0.289)$
$T(74)=37-6.065$
$T(74)=30.93\approx31^{\circ}$F
Therefore, on Day $74$, the temperature is $31^{\circ}$F.