HOW FAR IS THE HORIZON?

Say, you are travelling in a boat in a sea on a clear day. There is no dust, mist,or hills. You get a clear picture of environment. You see horizon. We say, horizon is the line where the sky meets the land. or the point where your straight line vision is blocked by earth's curvature. Now the question is , how far you can see?

You see the horizon with your eyes and your eyes are situated at 'your height' from the sea level. Let it be H. Let 'R' be the radius of the earth and 'D' be horizon distance from you. With this data, we have constructed a right angled triangle as shown in the figure.

APPLYING PYTHAGORAS THEOREM
R^2+D^2 = (R+H)^2
SIMPLIFYING,
D = ROOT OF(2RH)
putting radius of the earth R as 6.4*10^6 meters, we get D= square root of 2*6.4*10^6*H meters
suppose your height is 1.8 meters
D= 4800 meters or 3 miles.
Your horizon is at the distance of 3 miles.

Hence horizon goes further and further as you climb up and up.
Suppose, you go to the top of a hill, that is 180 meters high, you can see area of 30 miles radius. Put H=180 m in the formula . From the world's tallest building, the burj khalifa in Dubai, you can see for 102 kilometers. From mount Everest, you might see 336 kilometers. That is why captain of a ship, policeman, securities, go to the top and watch with binoculars. Again, an interesting application using Pythagoras theorem.

FOOT NOTE: As you go high above, you get a bird's eye view. Your world gets smaller. As you go spiritually high above, your problems get smaller and vanish.
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