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For an observer atop Mount Everest (8,848 metres (29,029 ft) in altitude), the horizon is at a distance of 336 kilometres (209 mi). For an observer aboard a commercial passenger plane flying at a typical altitude of 35,000 feet (11,000 m), the horizon is at a distance of 369 kilometres (229 mi).
Altitude (alt.), sometimes referred to as elevation (el.) or apparent height, is the angle between the object and the observer's local horizon. For visible objects, it is an angle between 0° and 90°. [b] Azimuth (az.) is the angle of the object around the horizon, usually measured from true north and increasing eastward.
[The percentage error, which increases roughly in proportion to the height, is less than 1% when H is less than 250 km.] With this calculation, the horizon for a radar at a 1-mile (1.6 km) altitude is 89-mile (143 km). The radar horizon with an antenna height of 75 feet (23 m) over the ocean is 10-mile (16 km).
An equation which finds the sine, followed by the arcsin function, is recommended when calculating latitude/declination/altitude. Azimuth (A) is referred here to the south point of the horizon, the common astronomical reckoning. An object on the meridian to the south of the observer has A = h = 0° with this usage.
An example of slant range is the distance to an aircraft flying at high altitude with respect to that of the radar antenna. The slant range (1) is the hypotenuse of the triangle represented by the altitude of the aircraft and the distance between the radar antenna and the aircraft's ground track (point (3) on the earth directly below the aircraft).
Assuming a perfect sphere with no terrain irregularity, the distance to the horizon from a high altitude transmitter (i.e., line of sight) can readily be calculated. Let R be the radius of the Earth and h be the altitude of a telecommunication station. The line of sight distance d of this station is given by the Pythagorean theorem;
In astronomy, the altitude in the horizontal coordinate system and the zenith angle are complementary angles, with the horizon perpendicular to the zenith. The astronomical meridian is also determined by the zenith, and is defined as a circle on the celestial sphere that passes through the zenith, nadir, and the celestial poles .
In practice it is not necessary to use zenith distances, which are 90° minus altitude, as the calculations can be done using observed altitude and calculated altitude. Taking a sight using the intercept method consists of the following process: Observe the altitude above the horizon Ho of a celestial body and note the time of the observation.