SOLUTION: theo looking up at a building in the distance. the angle of elevation to the top of the building is 20. he walks 200 feet closer and re-measures the angle to be 24. how tall is the

Algebra ->  Trigonometry-basics -> SOLUTION: theo looking up at a building in the distance. the angle of elevation to the top of the building is 20. he walks 200 feet closer and re-measures the angle to be 24. how tall is the      Log On


   

Question 1083795: theo looking up at a building in the distance. the angle of elevation to the top of the building is 20. he walks 200 feet closer and re-measures the angle to be 24. how tall is the building? answer
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  Make a sketch.


2.  Recall what the tangent is (I mean the Trigonometry function tan).



3.  Let H be the height of the building.

    Then the longest distance from Theo to the building was H%2Ftan%2820%29.

    Next, the closest distance from Theo to the building was H%2Ftan%2824%29.


    Your equation is H%2Ftan%2820%29+-+H%2Ftan%2824%29 = 200,   or

    H%2A%281%2Ftan%2820%29+-+1%2Ftan%2824%29%29 = 200.


    Solve it for H:

    H = 200%2A%281%2Ftan%2820%29+-+1%2Ftan%2824%29%29.



4.  You do the calculations.