Question

HELP PLEASE!!!!!! Th angle of elevation to the top of a building is 21 degrees. At a point 80 feet closer, the angle of elevation to the top of the same building is 33 degrees. Approximate the height of the building.

Answer 1

\[since:\tan 33 = h/x \]
\[\therefore h = x \tan 33\] --->1
\[since \tan 21 = h / (80+x)\]
\[\therefore h = (80+x)\tan 21\]---->2
\[solve 1 & 2 together\]

\[xtan33=80\tan21+xtan21\]
\[-80\tan21 = -xtan33+xtan21\]
\[80 \tan21= x(\tan33-\tan21)\]
\[x=115.6462729 substitue In ---->1\]
\[h= 75.10156777 feets \approx 75.1 feets\]