SOLUTION: From the top of an office building 72 ft high, the angle of elevation to the apartment building across the street is 31o. From the base of the office building, the elevation is 46o

Algebra ->  Trigonometry-basics -> SOLUTION: From the top of an office building 72 ft high, the angle of elevation to the apartment building across the street is 31o. From the base of the office building, the elevation is 46o      Log On


   

Question 43173: From the top of an office building 72 ft high, the angle of elevation to the apartment building across the street is 31o. From the base of the office building, the elevation is 46o. How tall is the apartment building.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
From the top of an office building 72 ft high, the angle of elevation to the apartment building across the street is 31o. From the base of the office building, the elevation is 46o. How tall is the apartment building.
Let a rectangle represent the office building (ob).
Let the base be "y".
Draw a higher rectangle adjacent on the right to the office building.
It is the apartment building (ab). Let the distance from the top of
ob to the top of ab be "x" ft.
From the top left corner of the ob draw a line rising 31 degrees
to the top of the ab.
From the bottom left corner of the ob draw a line rising 46 degrees
to the top of the ab.
You now have two equations:
tan(31 degrees) = x/y or y=x/tan(31 degrees)
tan(46 degrees) = (x+72)/y or y=(x+72)/tan(46 degrees)
Combining these you get:
x/tan31 = (x+72)/tan46
Solve for "x":
x/0.60086 = (x+72)/1.0355
1.0355x = 0.60086x+43.2619
0.43464x = 43.2619
x=99.535 ft.
Apartment building height is 72 +99.535 ft =171.53 ft
Cheers,
Stan H.
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