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Altitude (triangle) The three altitudes of a triangle intersect at the orthocenter, which for an acute triangle is inside the triangle. In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the side opposite the vertex. This line containing the opposite side is called the extended base ...
A star has an altitude above the horizon for an observer if the star is visible. Observing the same star at the same time from two different latitudes gives two different altitudes. Using geometry, the two altitudes along with the distance between the two locations allows for a calculation of Earth's size.
A triangle with all interior angles measuring less than 90° is an acute triangle or acute-angled triangle. [2] If c is the length of the longest side, then a 2 + b 2 > c 2, where a and b are the lengths of the other sides. A triangle with one interior angle measuring more than 90° is an obtuse triangle or obtuse-angled triangle. [2]
In Euclidean geometry, the geometric mean theorem or right triangle altitude theorem is a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that the geometric mean of the two segments equals the altitude. If h denotes the altitude in a right triangle and p and q ...
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
That premise is the basis for the most commonly used method of celestial navigation, referred to as the "altitude-intercept method." At least three points must be plotted. The plot intersection will usually provide a triangle where the exact position is inside of it. The accuracy of the sights is indicated by the size of the triangle.
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