A $25\mathrm{.}3kg$ person climbs up a uniform ladder with negligible mass. The upper end of the ladder rests on a frictionless wall. The bottom of the ladder rests on a floor with a rough surface where the coefficient of static friction is $0\mathrm{.}25.$ The angle between the horizontal and the ladder is $.$ The person wants to climb up the ladder a distance of $0\mathrm{.}85m$ along the ladder from the ladder's foot.

What is the minimum angle ${}_{\text{m}\text{i}\text{n}}($between the horizontal and the ladder$)$ so that the person can reach a distance of $0\mathrm{.}85m$ without having the ladder slip? The acceleration of gravity is $9\mathrm{.}8\frac{m}{s^2}.$

Answer in units of $.$ Answer in units of $.$

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$$#$1\mathrm{.}56\mathrm{.}5$