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When I give my answer below as the distance to the column, I am assuming that the dome fits perfectly on the column,
Thank you. I did not mean that his line of sight passed through the very top, I merely said "grazes the upper surface" (ie a tangent)
Unless I'm mistaken you seem to have missed what the problem is asking.
Because the circle sits at eye-level, and also has the 40° line grazing its upper surface, then a line at 20° (half of 40°) would go thru the circles center.
Egads and Gazooks! Give me a coupla days!
A cylindrical tower 7.5m high is surmounted by a dome 6m in diameter, on the top of which is a spike. A boy whose eye is 1.5m from the ground can just see the tip of the spike over the curve of the dome when his line of sight is at an elevation of 40°.Calculate the length of the spike and the distance the boy is from the nearest point of the tower.