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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