Answer
sin$\angle$FCH = $\frac{1}{\sqrt 3}$
cos $\angle$FCH = $\frac{\sqrt 2}{\sqrt 3}$
Work Step by Step
CH=$\sqrt CD^{2} + DH^{2}$
=$\sqrt 5^{2}+ 5^{2}$
=5$\sqrt 2$
CF=$\sqrt CH^{2} + HF^{2}$
=$\sqrt (5\sqrt 2)^{2}+ 5^{2}$
=5$\sqrt 3$
sin$\angle$FCH= $\frac{HF}{CF}$ = $\frac{5}{5\sqrt 3}$ = $\frac{1}{\sqrt 3}$
cos $\angle$FCH= $\frac{CH}{CF}$ = $\frac{5\sqrt 2}{5\sqrt 3}$ = $\frac{\sqrt 2}{\sqrt 3}$
