Answer
$\dfrac{5}{4}$
Work Step by Step
$45^o$ is a special angle whose sine value is $\dfrac{\sqrt2}{2}$.
$30^o$ is a special angle whose cosine value is $\dfrac{\sqrt3}{2}$
Thus,
$\sin^2{45^o} + \cos^2{30^o}
\\= \left(\dfrac{\sqrt2}{2}\right)^2 + \left(\dfrac{\sqrt3}{2}\right)^2
\\=\dfrac{2}{4} + \dfrac{3}{4}
\\=\dfrac{5}{4}$
