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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?

Guest May 13, 2017

Best Answer 

 #1
avatar+7336 
+4

 

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

 

\(\frac{CD}{\tan36}=\frac{CD}{\tan20}-600 \\~\\ \frac{CD}{\tan36}-\frac{CD}{\tan20}=-600 \\~\\ CD(\frac1{\tan36}-\frac1{\tan20})=-600 \\~\\ CD=-600\div(\frac1{\tan36}-\frac1{\tan20}) \\~\\ CD \approx 437.606 \text{ meters}\)

hectictar  May 13, 2017
 #1
avatar+7336 
+4
Best Answer

 

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

 

\(\frac{CD}{\tan36}=\frac{CD}{\tan20}-600 \\~\\ \frac{CD}{\tan36}-\frac{CD}{\tan20}=-600 \\~\\ CD(\frac1{\tan36}-\frac1{\tan20})=-600 \\~\\ CD=-600\div(\frac1{\tan36}-\frac1{\tan20}) \\~\\ CD \approx 437.606 \text{ meters}\)

hectictar  May 13, 2017
 #2
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+1

Thank you very much!

Guest May 13, 2017

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