#### Answer

$57^{\circ}$F

#### Work Step by Step

For Day $200$, we substitute $x=200$ in the formula:
$T(200)=37+21\sin[\frac{2\pi}{365}(x-91)]$
$T(200)=37+21\sin[\frac{2\pi}{365}(200-91)]$
$T(200)=37+21\sin[\frac{2\pi}{365}(109)]$
$T(200)=37+21\sin[1.876]$
$T(200)=37+21(0.954)$
$T(200)=37+20.03$
$T(200)=57.03\approx57^{\circ}$F
Therefore, on Day $200$, the temperature is $57^{\circ}$F.