[填空题]
A picnic area is shaped like a quh/ 0q + gwq8i,mwunq+xadrilate equ+-8qxsy:v ral, ABCD, where AB = 10 m andCD = 17.5 m. Three of the internal angles hav+uyqxs-8qve: e been measured; angle $\mathrm{A}\hat{\mathrm{D}}\mathrm{C}=51^{\circ}$, angle $\mathrm{C}\hat{\mathrm{A}}\mathrm{D}=70^{\circ}$ and angle $\mathrm{A}\hat{\mathrm{C}}\mathrm{B}= 42^{\circ}$. This information is represented in the following diagram.
1.Calculate the distance AC. m
2.Calculate the angle $\mathrm{A}\hat{\mathrm{B}}\mathrm{C}$. $^{\circ}$
There is a lamp post at A, perpendicular to the ground. The angle of elevation to the top of the lamp post from B is $32^{\circ}$.
3.Calculate the height of the lamp post. m
Patrick's family is having a barbecue party on the picnic area. The family brings a 1.5 litre bottle of lemonade and cone-shaped paper cups.
Each cup has a vertical height of 88 cm and the top of the cup has a diameter of 5 cm.
4.Calculate the volume of one paper cup. $cm^3$
5.Calculate the maximum number of cups that can be completely filled with the 1.5 litre bottle of lemonade. completely filled cups
