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.
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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
