本题目来源于试卷: Geometry & Shapes，类别为 IB数学
[问答题]
In a triangle $ \mathrm{XYZ}, \mathrm{XY}=9 \mathrm{~cm}, \mathrm{YZ}=x \mathrm{~cm}, \mathrm{XZ}=y \mathrm{~cm} $ and $\mathrm{XY} \mathrm{Y}=45^{\circ}$ .
1. Using the cosine rule, show that $x^{2}-9 \sqrt{2} x+81-y^{2}=0$.
Consider the possible triangles with $\mathrm{XZ}=7 \mathrm{~cm}$ .
2. Calculate the two corresponding values of Y Z .
3. Hence find the area of the smaller triangle.
Consider the case where y , the length of [X Z] , is not fixed at $ 7 \mathrm{~cm}$.
4. Find the range of values of y for which it is possible to form two triangles.
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