Earth's radius is about 4000 mi. To the nearest mile, what is the distance a person can see on a clear day from an airplane 5 mi above the Earth?
200 mi
63 mi
4000 mi
5660 mi

Draw a diagram. You want to see how far the horizon is from height h. Draw a radius extended by h. Draw the tangent to the circle from that extended radius. Draw a radius to the tangent. Now you have a right triangle with one leg=r, the hypotenuse=r+h.

If the distance to the horizon is d, then

r^2 + d^2 = (r+h)^2

4000^2 + d^2 = 4005^2

d^2 = 16040025 - 16000000 = 40025

d = 200 mi.

If r is very large compared to h, then we have

(r+h)^2 = r^2 + 2rh + h^2

but h^2 is negligible.

so, d^2 = 2rh = 2*4000*5 = 40000

d = 200

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this