Answer: [tex]54.508^{\circ}[/tex]
Step-by-step explanation:
Let the angle ADC = x degree
Since, By the given diagram, In triangle BDC,
[tex]\frac{BC}{DC} = tan27^{\circ}[/tex]
⇒ [tex]\frac{BC}{19.6} = tan27^{\circ}[/tex]
⇒ [tex]BC = 19.6\times tan 27^{\circ}[/tex]
⇒ [tex]BC = 9.98669881009[/tex]
Now, In triangle ADC,
[tex]tan x =\frac{AC}{DC}[/tex]
⇒ [tex]tan x =\frac{AB+BC}{DC}[/tex]
⇒ [tex]tan x =\frac{17.5+9.98669881009}{19.6}[/tex]
⇒ [tex]tan x =\frac{27.4866988101}{19.6}[/tex]
⇒ [tex]tan x =1.40238259235[/tex]
⇒ [tex]x = 54.508389368\text{ degree} \approx 54.508^{\circ}[/tex]
