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 \(\theta\)
In ΔABC,
tan\(\theta\) = \(\frac{\text Perpendicular}{\text Base}\)
tan\(\theta\) = \(\frac{h}{2x}\) ......(1)
In ΔDEC,
tan\(\theta\) = \(\frac{\text Perpendicular}{\text Base}\)
tan\(\theta\) = \(\frac{38}{x}\) ......(2)
Comparing (1) and (2) ,
\(\frac{h}{2x}\) = \(\frac{38}{x}\)
\(h=2\times38\)
⇒ \(h=76\)
Thus, Height of building is 76 feet.
