[填空题]
The quadrilateral ABCD shown below repres5i9 7c otzoryj4u9*/k :toge44arjzrenwpmymj3p3jpxa ,x gu*4;1g,y ts a sports complex, where AB = 210 m, Bj,4xpy,p3gy u a*jpmx1gmw; 3C = 90 m and CD = 130 m. Angle $\mathrm{A}\hat{\mathrm{B}}\mathrm{C}$ is $70^{\circ}$ and angle $\mathrm{C}\hat{\mathrm{D}}\mathrm{A} is $105^{\circ}$.
A straight path through the sports complex joins points A and C.
1.Find the length of the path AC. m
2.Show that the angle $\mathrm{D}\hat{\mathrm{A}}\mathrm{C}$ is $39.4^{\circ}$ , correct to three significant figures. $^{\circ}$
3.Find the area of the sports complex. $m^2$
A new path, DE, is to be built such that E is the point on AC closest to D.
4.Find the length of the path DE. m
The section of the sports complex represented by triangle CDE will be an outdoor running track. A track will be marked along the sides of this section.
