determine the height of the flagpole if the first angle of elevation is 18dgr than moved 50m and take the second one as 26dgr

Question

from the point on horizontal ground a surveyor measures the angle of elevation of the top of a flagpole as 18 degree. he moves 50 metre near to the flagpole and measure the angle of elevation as 26 degree . determine the height of the flagpole

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