determinnig the height of the flagpole using the following information

Question

From the point on the horizontal ground a surveyor measures the angle of the elevation of the top pole as 18 degree.he moves 50m nearer to the flagpole and measures the angle of elevation as 26 degree .determine the height of the flagpole?.

showing and explaining the method on how to come up with the solution willbe useful to me.

Answer 1

Let the distance from the pole be x. The height of the pole we'll call h.  So h/x=tan18; h/(x-50)=tan26 after he moves 50m nearer to the pole. x=hcot18, so we can write h/(hcot18-50)=tan26. This is an equation with only one unknown, h. So h=(hcot18-50)tan26, h(cot18tan26-1)=50tan26=24.3866 approx. and h=24.3866/0.5011=48.6675m approx.

CHECK

x=149.783 approx and h/x=tan18. x-50=99.783 and h/99.783=tan26.