Measure the elevation angle. At the elevation angle A from the geodesic plane to the spire at the distance of X meters from the tower, walk Y meters along the straight line connecting the tower with the measuring point (measure Y with a tape measure), and then measure the elevation angle B from the geodesic plane to the spire. So we know a, b, y. Let the tower height be h, then tanA=h/x and tanB=h/(x+y). The unknowns in these two equations are only X and H, so that h=ytanAtanB/(tanA-tanB) can be solved.