Problema Solution
An antenna 25 ft tall stands on top of a (flat-roofed) building. From a point on the ground, the angles of elevation to the top and the bottom of the antenna are 58 degrees and 47 degrees respectively. Find the height of the building (without the antenna).
Answer provided by our tutors
let 'd' represent the distance in feet from the point of observation to the base of the building and let 'h' represent the height in feet of the building without the antenna
tan(47) = h/d
tan(58) = (h+25)/d
tan(47)/tan(58) = (h/d)/((h+25)/d)) = h/(h+25)
solving for 'h' we have h=41.64
the height of the building is approximately 42 feet