The angles of elevation of an artificial satellite measured from two earth stations are $30^0$ and $40^0$ respectively. If the distance between the earth stations is 4000 km, then the height of the satellite is

Let h be the height of the satellite from the ground, and x be the horizontal distance from the first station to the point directly below the satellite. We have the equations tan(30) equals h divided by x and tan(40) equals h divided by (x minus 4000). Solving this system yields h equals 4000 multiplied by tan(30) multiplied by tan(40) divided by (tan(40) minus tan(30)). Calculating this with the given values of tan(30) at 0.577 and tan(40) at 0.839 gives a height of approximately 3464 km.

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