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An engineer estimates the angle of elevation to the top of the building to be 50°. After moving 1.5 meters further away, the angle of elevation was 40°. How high is the top of the building?

 May 5, 2017
 #1
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An engineer estimates the angle of elevation to the top of the building to be 50°.
After moving 1.5 meters further away, the angle of elevation was 40°.
How high is the top of the building?

 

(1)tan(50)=hxx=htan(50)(2)tan(40)=h1.5+xtan(40)=h1.5+htan(50)tan(40)(1.5+htan(50))=h1.5tan(40)+htan(40)tan(50)=hhhtan(40)tan(50)=1.5tan(40)h(1tan(40)tan(50))=1.5tan(40)h(tan(50)tan(40)tan(50))=1.5tan(40)h=1.5(tan(50)tan(40)tan(50)tan(40))h=1.5(1.191753592590.839099631181.191753592590.83909963118))h=1.5(10.35265396142)h=1.52.83564090981h=4.25346136471 m

 

The top of the building is 4.25 m high.

 

laugh

 May 5, 2017
edited by heureka  May 5, 2017

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