Geometry & Shapes (id: a67a568d8)

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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