本题目来源于试卷: Geometry & Shapes，类别为 IB数学
[问答题]
Peggy owns a rectangu(gh7eyz) +82 oaqnljclar field, jx(n) n98po vd 12 $\mathrm{~m} $ by 5 $\mathrm{~m}$ . Peggy attaches a rope to a metal post at the upper left corner of her field, and attaches the other end to her cow Daisy.
1. Given that the rope is 6 $\mathrm{~m} $ long, calculate the percentage of Peggy's field that Daisy is able to graze. Give your answer correct to the nearest percent.
2. Peggy replaces Daisy's rope with another one of length $\alpha \mathrm{m}, 5<\alpha<12$ , so that Daisy can now graze exactly three quarters of Peggy's field.
Show that $\alpha$ satisfies the equation
5 $\sqrt{\alpha^{2}-25}+\alpha^{2} \arcsin \left(\frac{5}{\alpha}\right)=90$
3. Find the value of $\alpha$ .
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