Hello stevekis the centre of the earth, whose radius isNow I am assuming that we are given
height of observer above surface of earth
height of part of tower not visible below the horizon. It is that we need to calculate.
is a point on the horizon visible from ; therefore is a tangent to the circle at , and
and are the angles (in radians) subtended at by the arcs ; therefore the arc lengths and are and respectively. If s is the total length of the arc ST, then:
...(1)(the radius of the earth),Therefore, in :
(the height of the observer) and
(the distance measured around the surface of the earth from the foot of the observer to the foot of the tower).
This, then, together with equations (1) and (2) will give you the height of the part of the tower below the visible horizon.
I've done a calculation on a spreadsheet (see second attachment) given:(radius of earth in m)which gives
(distance 100 km away)
(height of observer in m)
m.Seems OK to me.