from a building 60m high the angle of depression of the top n bottom of lamp post are 30 and 60 find thedistance betwwen lamp post and building aslo find the difference of height betwen buildingn lamp

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First we can use the steep triangle, the one from the building to the bottom of the lamp to find the distance from the lamp to the building, which I will call x meters.  We know that if we use the angle of depression, which is 60°, then we can use the top of the triangle as the distance, and Tangent of the angle of depression will be opposite/adjacent, or 60 meters/ x meters. tan(60°) = 60/xx*tan(60) = 60x*(sqrt(3)) = 60x = 60/sqrt(3)    = 20*sqrt(3)(or we could just use the rule of 30-60-90 triangles and know that the long side should be sqrt(3) times the short side.)Now we find the difference between heights by making the small triangle with the long side as the distance from the top of the lamp post to the building, and the short side would be y meters.tan(30) = y/(20*sqrt(3))(1/sqrt(3))*20*sqrt(3) = y          #sqrt(3)s cancely = 20 meters.Sorry, this is really confusing to explain without drawing pictures :-(