Answer:
Height of building is 76 feet.
Step-by-step explanation:
In the figure below,
AB is the building , DE is the tree standing in half way between the state and building.
Let angle at C be [tex]\theta[/tex]
In ΔABC,
tan[tex]\theta[/tex] = [tex]\frac{\text Perpendicular}{\text Base}[/tex]
tan[tex]\theta[/tex] = [tex]\frac{h}{2x}[/tex] ......(1)
In ΔDEC,
tan[tex]\theta[/tex] = [tex]\frac{\text Perpendicular}{\text Base}[/tex]
tan[tex]\theta[/tex] = [tex]\frac{38}{x}[/tex] ......(2)
Comparing (1) and (2) ,
[tex]\frac{h}{2x}[/tex] = [tex]\frac{38}{x}[/tex]
[tex]h=2\times38[/tex]
⇒ [tex]h=76[/tex]
Thus, Height of building is 76 feet.
