a^2 + b^2 = c^2
8^2 + b^2 = 19^2
64 + b^2 = 361
b^2 = 361 - 64
b^2 = 297
b = [tex]\sqrt{297}[/tex]
b = 3[tex]\sqrt{33}[/tex] which is the segment AB
a^2 + b^2 = c^2
8^2 + b^2 = 11^2
64 + b^2 = 121
b^2 = 121 - 64
b^2 = 57
b = [tex]\sqrt{57}[/tex] which is the segment DB
Subtract segment DB from segment AB in order to find the length of segment AD.
3[tex]\sqrt{33}[/tex] - [tex]\sqrt{57}[/tex] ≈ 9.684
Answer: 9.7 or 9.68 or 9.684 or 10 (depending on what your teacher wants as approximate answer)
