Question

A tower has an observation deck about 200 m above ground level. About how far is it from the observation deck horizen knowing that the earth's radius is 6400km?

Answer 1

Answer: Horizon is 35777.64 m away from observation deck.

Step-by-step explanation:

Since we have given that

Height of tower above ground level = 200 m

Radius of earth = 6400 km

Let R be the radius of earth.

Let the height of observation and

Let d be the distance from observation deck to horizon.

so, it makes a right angle triangle.

$(R+h)^2=R^2+d^2\\\\R^2+h^2+2Rh=R^2+d^2\\\\h^2+2Rh=d^2\\\\200^2+2\times 6400000\times 200=d^2\\\\40000+1280040000=d^2\\\\1280040000=d^2\\\\\sqrt{1280040000}=d\\\\d=35777.64\ km$

Hence, horizon is 35777.64 m away from observation deck.

Answer 2

Answer:

He is a a distance of 50.597 km from the observable deck of horizon.

Step-by-step explanation:

The distance from a height 'h' to the observable horizon ignoring the effects due to refraction in atmosphere is given by the formula

$d=\sqrt{h(2R+h)}$

where

d = distance to observable horizon

h = height of observer from the sea level

R = Radius of earth

Applying the values we get

$d=\sqrt{0.2\times (2\times 6400+0.2)}\\\\\therefore d=50.597km$