from the top of 50 metre high hill the angle of depression of the top and the bottom of a tower are 30°and45°.find the hight of the tower

Draw the diagram.

If the horizontal distance from the hill to the tower is x, then if the tower's height is h, we have

50/x = tan45
(50-h)/x = tan30

eliminating x, we get

50 cot45 = (50-h) cot30

Now just solve for h