His a point on the ground due east of a building, 72m high, and k is a point due west of the building. the angles of elevation of the top of the building from h and k are 43 degrees and 54 degrees respectively. find the actual distance of h and k from top of the building.

Let's consider the figure is a triangle, in which perpendicular is the Height of the building whereas actual distance of H and K from top of the building would be corresponding Hypotenuse.

Now, Sin Ф = P / H
Sin 43 = 72 / H
H = 72 / Sin 43
H = 72 / 0.68    [ Sin 43 = 0.68 ]
H = 105.88 meters 

Now, Sin 54 = 72 / H
K = 72 / Sin 54
K = 72 / 0.80
K = 90 meters

Hope this helps!