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Right Triangles Problem

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From a point 100 feet in front of a public library, the angles of elevation to the base of the flagpole and to the top of the flagpole are 28 degrees and 39.75 degrees, respectively. The flagpole is mounted on the roof of the library. Find the height of the flagpole.

Guest Apr 26, 2017
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Let  H  be the height of the flagpole  and B the height of the building

And we have that

tan (28)  = B / 100  →   100 tan (28)   = B      (1)

tan (39.75)  =   ( B + H) / 100   →   100 tan (39.75)  =  B + H     (2)

Sub (1)  into (2)

100 tan (39.75)  =    100 tan (28)  + H        rearrange

100 tan (39.75)   -  100 tan (28)   =   H

100 (tan (39.75)  - tan (28) )   =  H  ≈  30 ft

CPhill  Apr 27, 2017

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