Pythagorean theorem is used to develop the relationship between an antenna height and theoptical radio horizon (coverage range of the antenna) as clearly depicted in Fig 4.12 on page 139of the textbook.RadohorizonAntannaOptical hori zonEarthFigure 4.12 Optical and Radio Har izansThe antenna height (in meters) vs the coverage range relationship is provided asd = 3570 vh metersThis is based on an average Earth radius of Rg = 6371000 meters.Q1. Prove the above relationship.Q2. Calculate the coverage range d for antenna heights of h = 25 and 16 meters. You mayprovide d either in meters or in km.Now assume that we want to installa communication antenna on the surface of Moon.Q3. Derive a similar relationship between d and h for the surface of moon if Moon has anaverage radius of RM = 1738000 meters.Q4. Calculate the coverage range d on the surface of Moon for antenna heights of h = 25 and 16meters. You may provide d either in meters or in km.

Answered: Image /qna-images/answer/b969c87a-04ac-4128-9671-27bf0000c6a8.jpg

Pythagorean theorem is used to develop the relationship between an antenna height and the optical radio horizon (coverage range of the antenna) as clearly depicted in Fig 4.12 on page 139 of the textbook.

Pythagorean theorem is used to develop the relationship between an antenna height and the optical radio horizon (coverage range of the antenna) as clearly depicted in Fig 4.12 on page 139 of the textbook.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

Pythagorean theorem is used to develop the relationship between an antenna height and the
optical radio horizon (coverage range of the antenna) as clearly depicted in Fig 4.12 on page 139
of the textbook.
Radohorizon
Antanna
Optical hori zon
Earth
Figure 4.12 Optical and Radio Har izans
The antenna height (in meters) vs the coverage range relationship is provided as
d = 3570 vh meters
This is based on an average Earth radius of Rg = 6371000 meters.
Q1. Prove the above relationship.
Q2. Calculate the coverage range d for antenna heights of h = 25 and 16 meters. You may
provide d either in meters or in km.
Now assume that we want to installa communication antenna on the surface of Moon.
Q3. Derive a similar relationship between d and h for the surface of moon if Moon has an
average radius of RM = 1738000 meters.
Q4. Calculate the coverage range d on the surface of Moon for antenna heights of h = 25 and 16
meters. You may provide d either in meters or in km.

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