From a point A, Tommy notices that the angle of elevation of the top of a building is 20o. He moves 600 meters closer to the building and now measures the angle of elevation to be 36o. How tall is the building?
Here, CD is the height of the building.
tan 36º = CD / BC
BC tan 36º = CD
BC = CD / tan 36º
tan 20º = CD / (600 + BC)
(600 + BC) tan 20º = CD
BC = CD/tan 20º - 600
\(\frac{CD}{\tan36}=\frac{CD}{\tan20}-600 \\~\\ \frac{CD}{\tan36}-\frac{CD}{\tan20}=-600 \\~\\ CD(\frac1{\tan36}-\frac1{\tan20})=-600 \\~\\ CD=-600\div(\frac1{\tan36}-\frac1{\tan20}) \\~\\ CD \approx 437.606 \text{ meters}\)
Here, CD is the height of the building.
tan 36º = CD / BC
BC tan 36º = CD
BC = CD / tan 36º
tan 20º = CD / (600 + BC)
(600 + BC) tan 20º = CD
BC = CD/tan 20º - 600
\(\frac{CD}{\tan36}=\frac{CD}{\tan20}-600 \\~\\ \frac{CD}{\tan36}-\frac{CD}{\tan20}=-600 \\~\\ CD(\frac1{\tan36}-\frac1{\tan20})=-600 \\~\\ CD=-600\div(\frac1{\tan36}-\frac1{\tan20}) \\~\\ CD \approx 437.606 \text{ meters}\)