#### Answer

$58^{\circ}$F

#### Work Step by Step

Since June $25$ represents Day $175$, we substitute $x=175$ in the formula:
$T(175)=37+21\sin[\frac{2\pi}{365}(x-91)]$
$T(175)=37+21\sin[\frac{2\pi}{365}(175-91)]$
$T(175)=37+21\sin[\frac{2\pi}{365}(84)]$
$T(175)=37+21\sin[1.446]$
$T(175)=37+21(0.992)$
$T(175)=37+20.84$
$T(175)=57.84\approx58^{\circ}$F
Therefore, on Day $175$, the temperature is $58^{\circ}$F.