[填空题]
The sides of a triangle ABC have the following l 9rzkk6bu,n/j.ybad2engths AB = 40 mm, BC u tw 5,rd5-7 dq+att7pi h4lby= 30 mm, and CA = 55 7brut7y,5 p+ i wqd4-ldtth5amm.
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