Answer:
Hight of the statue [tex]=31.547m[/tex]
Step-by-step explanation:
[tex]AB=[/tex] Position of the building.
[tex]CD=[/tex] Position of the statue.
[tex]AC=[/tex] Distance between the building and statue
Angle of elevation of the top of the statue from the top of the building is ∠ [tex]DBE=30[/tex]°
Angle of depression of the bottom of the statue from the top of the building is ∠ [tex]EBC=45[/tex]°
From the figure, [tex]AC=BE, AB=CE, AC=20m.[/tex]
In the right angle triangle [tex]BDE,[/tex]
[tex]tan 30[/tex]°[tex]=[/tex] [tex]\frac{DE}{BE}[/tex]
[tex]DE=BE*tan30[/tex]°
[tex]=20*\frac{1}{\sqrt{3} }[/tex]
[tex]DE=11.547[/tex] This is our first equation.
In the right angle triangle [tex]EBC,[/tex]
[tex]tan45[/tex]°[tex]=\frac{CE}{BE}[/tex]
[tex]CE=BE*tan45[/tex]°
[tex]=20*1[/tex]
[tex]CE=20[/tex] This is our second equation.
Adding equations, we get
[tex]DE+CE=11.547+20[/tex]
[tex]CD=31.547[/tex]
Therefore hight of the statue [tex]=31.547m[/tex]