1-if a person's line of vision is at the top of Building 121 feet high, how far out to sea could a person see with a good telescope?
2- the light in a lighthouse is 144 feet above sea level. How far does the light extend before it dips below sea level?
3- if an observer is on a tower 144 meters high, how many kilometers out to sea, could a surfer be observed, using a powerful telescope?
There is more of Those kind questions.. Can anyone pleas give me a website that just i put the number and find out the solution.. Or give me the formal by answering these questions?
The formula in feet and miles is the square root of 1.5 x 121 feet. So -- your first answer is 13.47 miles. Check this site for more information and the formula for figuring the distance in meters and kilometers.
http://en.wikipedia.org/wiki/Horizon
from where did u get, and how 1.5
I found the formula in the web site I posted.
The formula for calculating the distance to the horizon is derived from the Pythagorean theorem. It states that the square of the distance to the horizon is equal to 1.5 times the height above sea level. This constant, 1.5, represents the average ratio of the radius of the Earth to the radius of Earth's atmosphere. It is used as an approximation in this calculation.
The formula used to calculate the distance to the horizon is derived from the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, the triangle is formed by the person's line of vision, the distance to the horizon, and the radius of the Earth.
The formula for calculating the distance to the horizon is:
d = √(2Rh + h^2)
where d is the distance to the horizon, R is the radius of the Earth, and h is the height of the observer above sea level.
The reason why 1.5 is used in the formula is that it is an approximation for the radius of the Earth in terms of units of the observer's height. It takes into account the curvature of the Earth and the refraction of light, which slightly increases the distance to the horizon.
The value of 1.5 is an approximation and may vary depending on various factors such as atmospheric conditions and the location on Earth. The website I mentioned, Wikipedia, provides more detailed information and alternative formulas for calculating the distance to the horizon in different units.
I hope this explanation helps you understand the formula and how to calculate the distance to the horizon in different scenarios.