What is the value of 5sin260° + 7sin245°+ 8cos245°?

Answer: Option C

$$\begin{array}{rl}& 5{\sin }^{2}60^{\circ }+7{\sin }^{2}45^{\circ }+8{\cos }^{2}45^{\circ }\\ & =5{\left(\frac{\sqrt{3}}{2}\right)}^2+7{\left(\frac{1}{\sqrt{2}}\right)}^2+8{\left(\frac{1}{\sqrt{2}}\right)}^2\\ & =\frac{15}{4}+\frac{7}{2}+\frac{8}{2}\\ & =\frac{15+14+16}{4}\\ & =\frac{45}{4}\end{array}$$