$$\sin ^ { 2 } 60 ^ { \circ } + \cos ^ { 2 } 45 ^ { \circ } + \tan ^ { 2 } 60 ^ { \circ }$$
$\frac{17}{4}=4.25$
$$\left(\frac{\sqrt{3}}{2}\right)^{2}+\left(\cos(45)\right)^{2}+\left(\tan(60)\right)^{2}$$
$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\left(\cos(45)\right)^{2}+\left(\tan(60)\right)^{2}$$
$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\left(\frac{\sqrt{2}}{2}\right)^{2}+\left(\tan(60)\right)^{2}$$
$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+\left(\tan(60)\right)^{2}$$
$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+\left(\sqrt{3}\right)^{2}$$
$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+3$$
$$\frac{\left(\sqrt{3}\right)^{2}+\left(\sqrt{2}\right)^{2}}{2^{2}}+3$$
$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+\frac{3\times 2^{2}}{2^{2}}$$
$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\frac{\left(\sqrt{2}\right)^{2}+3\times 2^{2}}{2^{2}}$$
$$\frac{3}{2^{2}}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+3$$
$$\frac{3}{4}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+3$$
$$\frac{3}{4}+\frac{2}{2^{2}}+3$$
$$\frac{3}{4}+\frac{2}{4}+3$$
$$\frac{3}{4}+\frac{1}{2}+3$$
$$\frac{5}{4}+3$$
$$\frac{17}{4}$$
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