[填空题]
The sides of a triangle ABC have the following lengths AB = 40 bb: n zez a2xx+ /kq4))jyd.r(gam5ocmm, BC = 30 mq.7pdqb zkr2 dz ,tci76mt0m(m, and CA = 55 mm.
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1.Calculate the size of the angle $\mathrm{A}\hat{\mathrm{B}}\mathrm{C}$. $^{\circ}$
2.Calculate the area of the triangle ABC. $mm^2$
A point D is located outside of the triangle, such that angle $\mathrm{D}\hat{\mathrm{A}}\mathrm{B}$ is $80^{\circ}$ and angle $\mathrm{D}\hat{\mathrm{B}}\mathrm{A}$ is $10^{\circ}$.
3.Show that the angle $\mathrm{A}\hat{\mathrm{D}}\mathrm{B}$ is $90^{\circ}$. $^{\circ}$
4.Find the distances AD and BD. mm
5.Find the shortest path which starts at point B and passes through all points A, C, D (in any order). mm
