geometry circles and triangles

Question

radius of the planet is 8400km the distance d to the horizon that can see on a clear day from the following height h above the planet .h= 3 km a person can see approximately how many km on a clear day from 3 km?

 

Answer 1

This site does not permit drawings, so I can only describe the solution.

 

Draw a circle. Place a dot at its center. Draw a vertical line from the center to the top of the circle. Label that line R. From the top of the circle, place a dot above the circle representing a height of 3Km. Label that line h. Draw line from h to a point that is tangent to the circle. Label that line d. Where the tangent line meets, the circle, draw line to the center. Label that line r.

 

You will now have a right triangle, whose dimensions can be obtained with the Pythagorean theorem.

In this case, (R + h)2 = r2 + d2

 

Rearranging and solving for d, we get d = square root (2•R•h)

 

d = square root of 2•8400•3 = 224.5Km