SOLUTION: Can someone help me solve this problem regarding some building's height? it goes like this: "Find the height of a building if the angle of elevation to the top of the buildin

Algebra ->  Trigonometry-basics -> SOLUTION: Can someone help me solve this problem regarding some building's height? it goes like this: "Find the height of a building if the angle of elevation to the top of the buildin      Log On


   

Question 1140020: Can someone help me solve this problem regarding some building's height? it goes like this:

"Find the height of a building if the angle
of elevation to the top of the building changes from 18° to 37°
as an observer moves a distance of 80 feet toward the building."

Figure regarding the height of the building:

https://i.imgur.com/2Zno0OW.png

As usual, thanks in advance!



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find the height of a building if the angle of elevation to the top of the building changes from 18° to 37° as an observer moves a distance of 80+feet toward the building.

observer moves a distance of 80 (from original point) feet toward the building, and rest of a distance to building is x
observe triangle with legs x and h(height)
=>tan+%28+37%29=h%2Fx
x=h%2Ftan+%28+37%29

total distance from the building is

x%2B80=h%2Ftan+%28+37%29%2B80

then triangle with legs x%2B80 and h

tan+%28+18%29=h%2F%28h%2Ftan+%28+37%29%2B80%29

%28h%2Ftan+%28+37%29%2B80%29%2Atan+%28+18%29=h

%28%28h%2Atan+%28+18%29%29%2Ftan+%28+37%29%29%2B80%2Atan+%28+18%29=h

h%28tan+%28+18%29%2Ftan+%28+37%29%29%2B80%2Atan+%28+18%29=h

h%28tan+%28+18%29%2Ftan+%28+37%29%29-h=-80%2Atan+%28+18%29

h%28tan+%28+18%29%2Ftan+%28+37%29-1%29=-80%2Atan+%28+18%29

h=%28-80%2Atan+%28+18%29%29%2F%28tan+%28+18%29%2Ftan+%28+37%29-1%29

h=45.7ft-> height of the building

then
x=45.7%2Ftan+%28+37%29=60.65ft
ad total distance is 80%2B60.65=140.65ft
check angles:
tan%5E-1%2845.7%2F60.65%29=37°
tan%5E-1%2845.7%2F140.65%29=18°...which confirms solution