Answer:
18.692
48.344
7.075
101.972
Step-by-step explanation:
19)
[tex]cos23=\frac{BD}{AB}\\\Rightarrow BD=cos23\times 29[/tex]
[tex]tan 55=\frac{BD}{DC}\\\Rightarrow tan 55=\frac{cos23\times 29}{x}\\\Rightarrow x=\frac{cos23\times 29}{tan55}\\\Rightarrow x=18.692[/tex]
x = 18.692
20)
[tex]tan68=\frac{AD}{BD}\\\Righarrow tan68=\frac{16}{BD}\\\Rightarrow BD=\frac{16}{tan68}[/tex]
[tex]cos35=\frac{BD}{BC}\\\Rightarrow cos35=\frac{\frac{16}{tan68}}{x}\\\Rightarrow x=\frac{\frac{16}{tan68}}{cos35}\\\Rightarrow x=48.344[/tex]
x = 48.344
21)
[tex]cos62=\frac{BD}{AB}\\\Rightarrow cos62=\frac{BD}{20}\\\Rightarrow BD=20\times cos62[/tex]
[tex]tan 37=\frac{DC}{BD}\\\Rightarrow tan 37=\frac{x}{20\times cos62}\\\Rightarrow x=tan37\times 20\times cos62\\\Rightarrow x=7.075[/tex]
x = 7.075
22)
[tex]tan24=\frac{AD}{BD}\\\Rightarrow tan24=\frac{47}{BD}\\\Rightarrow BD=\frac{47}{tan24}[/tex]
[tex]tan44=\frac{DC}{BD}\\\Rightarrow tan44=\frac{x}{\frac{47}{tan24}}\\\Rightarrow x=tan44\times \frac{47}{tan24}\\\Rightarrow x=101.972[/tex]
x = 101.972
A, B, C and D have been taken according to the diagram for all the triangles.
