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?
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∘))=h1.5⋅tan(40∘)+h⋅tan(40∘)tan(50∘)=hh−h⋅tan(40∘)tan(50∘)=1.5⋅tan(40∘)h⋅(1−tan(40∘)tan(50∘))=1.5⋅tan(40∘)h⋅(tan(50∘)−tan(40∘)tan(50∘))=1.5⋅tan(40∘)h=1.5⋅(tan(50∘)⋅tan(40∘)tan(50∘)−tan(40∘))h=1.5⋅(1.19175359259⋅0.839099631181.19175359259−0.83909963118))h=1.5⋅(10.35265396142)h=1.5⋅2.83564090981h=4.25346136471 m
The top of the building is 4.25 m high.