when doug looks at the top of a tower, ange of elevation is 27 degrees, when doug walks 20m further away from the tower on level ground, angle of elevation decreases to 20 degrees, what is the height of the tower?
+33659 tan(elevation) = height/distance
tan(27°) = height/distance (1)
tan(20°) = height/(distance+20) (2)
From (1) we have distance = height/tan(27°). Put this into (2):
tan(20°) = height/(height/tan(27°)+20) so
tan(20°)*(height/tan(27°) + 20) = height or
height*tan(20°)/tan(27°) + 20tan(20°) = height or
height(1 - tan(20°)/tan(27°)) = 20tan(20°) so
height = 20tan(20°)/(1 - tan(20°)/tan(27°))
You can do the number crunching!
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